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A post-compression based ultrasound imaging technique for simultaneous transmit multi-zone focusing
Ultrasonics 46 (2007) 148–154 www.elsevier.com/locate/ultras
A post-compression based ultrasound imaging technique for simultaneous transmit multi-zone focusing Bae-Hyung Kim, Gi-Duck Kim 1, Tai-Kyong Song
*
Department of Electronic Engineering, Sogang University, C.P.O. Box 1142, Seoul 110-611, Republic of Korea Received 27 November 2006; received in revised form 17 January 2007; accepted 19 January 2007 Available online 12 February 2007
Abstract The compression error of post-compression based coded excitation techniques increases with decreasing f-number, which causes the elevation of side-lobe levels. In this paper, a post-compression based coded excitation technique with reduced compression errors through dynamic aperture control is proposed. To improve the near-field resolution with no frame rate reduction, the proposed method performs simultaneous transmit multi-zone focusing using two mutually orthogonal complementary Golay codes. In the proposed method, the two mutually orthogonal sequences of length 16 are simultaneously transmitted toward two different focal depths, which are separately compressed into two short pulses on receive after dynamic focusing is performed. After carrying out the same transmit-receive operation for the same scan line with the complementary set of the orthogonal Golay codes, a single scan line with two transmit foci is obtained.The computer simulation results using a linear array with a center frequency of 7.5 MHz and 60% 6 dB bandwidth show that the range side-lobe level can be suppressed below 50 dB, when f-number is maintained not smaller than 3. The performance of the proposed scheme for a smaller f-number of 2 was also verified through actual experiments using a 3.85 MHz curved linear array with 60% 6 dB bandwidth. Both the simulation and experimental results show that the proposed method provides improved lateral resolution compared to the conventional pre-compressed and post-compression based coded excitation imaging using Golay codes. 2007 Elsevier B.V. All rights reserved. Keywords: Ultrasound Imaging; Coded excitation; Simultaneous; Post-compression; Golay codes
1. Introduction Conventional ultrasound pulse-echo imaging systems have limitations on transmitted energy due to peak power constraints for avoiding tissue damage. Hence, the conventional ultrasound imaging using short transmit pulses often suffer from low signal-to-noise-ratio (SNR) and small detection range. On the other hand, coded excitation, which employs pulse compression techniques, can improve the SNR of ultrasound imaging by increasing average power without affecting instantaneous peak power [1–5]. In coded ultrasound imaging, coded waveforms of a long
*
1
Corresponding author. Tel.: +82 2 705 8907; fax: +82 2 707 3008. E-mail address: [email protected] (T.-K. Song). Co-first author.
0041-624X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2007.01.007
duration are transmitted and the reflected signals are sampled and compressed into a high-amplitude short pulse. Ideally, pulse compression should be performed on the received signal samples on each channel prior to receive beamforming, which is called pre-compression [6,7]. This requires a pulse compressor per each channel, resulting in huge increase in system complexity. Therefore, post-compression, which performs pulse compression on focused RF data, is a very attractive approach, because it only requires a single compression hardware for the whole system. However, post-compression introduces compression error and accompanying degradation in spatial resolution since it is equivalent to performing pulse compression on the irregularly rearranged version (according to the dynamic focusing delay) of the received signal samples on each channel and summing up the resulting compressed signals for all channels.
B.-H. Kim et al. / Ultrasonics 46 (2007) 148–154
Among many coded signals, Golay codes have very attractive properties for medical ultrasound imaging since they consist of a pair of complementary sequences of 1 0 s and 1 0 s and sum of their autocorrelation functions is an impulse function [8]: they can be transmitted with a conventional bi-phase, high-voltage pulser, instead of a more expensive and larger linear power amplifier with low power efficiency, and the received signals can be converted into a short pulse with a high-peak and low range side-lobes using a correlator consisting only of 2 0 s complementary adders [9–12]. For these reasons, the Golay code pulse compression has found various applications in medical ultrasound imaging such as for improving SNR and penetration depth [1–5], spatial resolution based on synthetic aperture techniques with reduced motion artifact [6,13,14], performance of harmonic imaging with and without contrast agents [15– 18], and for reducing the system size [12]. A disadvantage of coded excitation imaging with Golay codes is that it requires two consecutive transmissions to obtain each scan line [10–12]. The resulting frame rate reduction will be harmful particularly when multiple transmit focusing, a conventional method to improve lateral resolution, is employed because it requires the same number of transmit-receive events as the number of transmit focal zones along each scan line [19]. To prevent the frame rate reduction, various imaging methods using orthogonal Golay codes have been studied [13,20–23]. Recently, the authors have suggested pre-compression based coded imaging techniques for simultaneous transmit multi-zone focusing (STMF) [12,22,23]. These methods can achieve multiple transmit focusing without sacrificing the imaging frame rate by transmitting the orthogonal Golay codes focused at different focal depths simultaneously, which can be separated and individually focused on receive using their orthogonal properties [22–25]. However, the pre-compression based coded excitation system using orthogonal Golay codes is not suitable for hand-held or small portable ultrasound systems, because it requires a correlator for each active channel to compress the received signals. This paper suggests a method for improving the spatial resolution by employing the post-compression based STMF using orthogonal Golay codes with reduced compression error. The following section starts with the investigation of an error introduced in post-compression scheme and describes the proposed post-compression based STMF method. The computer simulation and experimental results in Section 3 show the difference between pre- and post-compression schemes. Some conclusions are drawn in the last section.
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the time delay sn with respect to the depth z, which can be expressed as 2 3 " pffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 2 2 osn o z z þ xn 16 1 7 ¼ ¼ 41 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5 oz c c oz 2 1 þ ðxn =zÞ " # 1 1 z 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fn ¼ ¼ ; ð1Þ c 2xn 1 þ 1=4fn2 where c is the velocity of ultrasound and fn is the f-number for the nth element. It is worth noting that the range derivative of the value sn gets smaller for a larger f-number. Since the f-number is proportional to the depth and inversely proportional to xn, the compression error will be the highest for the outer-most element at the nearest depth. Fig. 1 shows the range sidelobe levels (RSLL) of the compressed waveforms for different f-numbers. It is obtained by performing post-compression on the dynamically focused signals from a target at 1 cm when Golay codes of length 2.2 ls are transmitted toward a transmit focus at 1 cm from a 7.5 MHz linear array with element spacing of 0.2 mm. One can see that the compression error leads to increase in RSLL, which decreases with increasing f-number. Therefore, the f-number must be kept larger than a proper value to suppress the compression error below a desired level. For example, to keep the RSLL below 50 dB in Fig. 1, the f-number should not be smaller than 3. Now it becomes obvious that the post-compression based ultrasound beamforming cannot avoid the degradation of spatial resolution due to the f-number limitation. In practice, the f-number starts decreasing from a certain depth, where the number of active elements, which increases with depth, reaches to the pre-determined maximum value. Hence, the problem of limited f-number in post-compression based beamforming will be dominant in the near field.
2. Post-compression based STMF imaging method using orthogonal Golay codes Post-compression introduces errors when dynamic receive focusing is employed [2,9,26]. The amount of the error depends on how fast the delay profile for dynamic focusing changes. Specifically, the compression error for the nth element at xn increases with the rate of change of
Fig. 1. Compressed waveforms of Golay codes of duration 2.2 ls for various f-numbers when post-compression is employed. A 7.5 MHz linear array with element spacing of 0.2 mm is used to transmit the Golay codes toward a point target located at the transmit focus (F = 1 cm).
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N
Correlator A1 Correlator A2 Correlator B1 Correlator B2
TGC N Beamformer /ADC
Zone blending
1st Tx: Orthogonal Golay codes (A1, B1) N pulser
transducer
modulation m(t)
Tx delay controller 2nd Tx: Complementary set of the Orthogonal Golay codes (A2, B2)
Fig. 2. System block diagram to implement the proposed method.
Fig. 2 shows the block diagram of the proposed postcompression based transmit multi-zone focusing method to improve the near-field resolution using two sets of mutually orthogonal Golay sequences of, [A1(n), A2(n)] and [B1(n), B2(n)], which satisfy the followings due to their orthogonal and complementary properties [24,25] ½A1 ðnÞ þ B1 ðnÞ A1 ðnÞ þ ½A2 ðnÞ þ B2 ðnÞ A2 ðnÞ ¼ A1 ðnÞ A1 ðnÞ þ A2 ðnÞ A2 ðnÞ ¼ 2LdðnÞ
ð2aÞ
½A1 ðnÞ þ B1 ðnÞ B1 ðnÞ þ ½A2 ðnÞ þ B2 ðnÞ B2 ðnÞ ¼ B1 ðnÞ B1 ðnÞ þ B2 ðnÞ B2 ðnÞ ¼ 2LdðnÞ
ð2bÞ
where L is the length of Golay codes and represents the relative time duration of the transmitted signal compared to that of a conventional on-off signal. In the first transmit-receive (T/R) event, A1(n) and B1(n) are added together with delays s(F1) and s(F2) for two different focal points F1 and F2, respectively. The combined code is then modulated by a proper function m(t) to be matched to the passband of the imaging transducer [12,27] before being transmitted simultaneously. On receive, the returned signals are dynamically focused and then correlated with each of the modulated codes. The same T/R event is repeated along the same scan line with A2(n) and B2(n). The transmitted signals from the kth array element can be represented as L1 X fAi ðnÞdðt sk ðF 1 Þ nT Þ fik ðtÞ ¼ mðtÞ n¼0
þ Bi ðnÞdðt sk ðF 2 Þ nT Þg;
i ¼ 1; 2
ð3Þ
where L represents the code length, T = 1/f0, and the transducer response is ignored for the convenience of analysis. If we consider the case where two point targets are located at the two transmit foci, the output of receive beamformer can be expressed approximately as ri ðtÞ ¼ mðtÞ
L1 X i ðnÞdðt sðF 1 Þ nT Þ fA n¼0
i ðnÞdðt sðF 2 Þ nT Þg; þB
i ¼ 1; 2
ð4Þ
i ðnÞ and B i ðnÞ represent the dynamically focused sewhere A quences, and s(Fi) denotes the propagation delay from the array center to each transmit focus. Now that the modulated
PL1 signals are givenP by mi;A ðtÞ ¼ mðtÞ n¼0 Ai ðnÞdðt nT Þ and L1 mi;B ðtÞ ¼ mðtÞ n¼0 Bi ðnÞdðt nT Þ, the two correlators in Fig. 2 produce ri(n)*m1 (n) and ri(n)*m2(n) in each T/R cycles. Now, lets assume that the compression error resulting from dynamic focusing in the post-compression scheme can be neglected due to the proper f-number control. Then, it is easy to show that two focused beams along the same scan line are obtained by using the orthogonal and complementary properties of Eqs. (2a) and (2b) as follows: r1 ðtÞ m1;A ðtÞ þ r2 ðtÞ m2;A ðtÞ 2L mðt sðF 1 ÞÞ mðtÞ r1 ðtÞ m1;B ðtÞ þ r2 ðtÞ m2;B ðtÞ
ð5aÞ
2L mðt sðF 2 ÞÞ mðtÞ
ð5bÞ
Finally, by combining the two beams based on the conventional beam blending method, a scan line with two transmit foci is obtained. Consequently, a frame of image with improved resolution is obtained at the same frame rate as that of the conventional pre-compression based single-zone transmit focusing method using Golay codes. It should be noticed that compared to the pre-compression method the proposed post-compression method can save 2(N 1) correlators, where N represents the number of active channels. 3. Experimental results To evaluate the performance of the proposed STMF method based on post-compression, experiments with computer generated signals and actual data acquired from a commercial ultrasound scanner are performed. In all experiments, Golay codes of length 16 generated by using the method in [24,27] are used. In the computer simulation study using Field II [28], a linear array with the center frequency of 7.5 MHz and element pitch of 0.2 mm is used, and the number of scan lines and the maximum number of active channels are assumed to be 192 and 64, respectively. The first transmit focus is set to 20 mm for a near zone up to 38 mm and the second to 50 mm. Since the minimum f-number is chosen to be 3, 64 elements are used from the depth 38 mm. Fig. 3 shows the computer generated B-scan images (dynamic range: 60 dB) of several point
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Fig. 3. Computer generated point target images by various methods: (a) pulse-echo imaging with a single transmit focus at 3 cm, (b) pre-compression based STMF with two transmit foci at 2 cm and 5 cm, (c) post-compression based STMF with transmit foci at 2 cm and 5 cm, and (d) difference between the two images (b) and (c).
targets by using the conventional single zone transmit focusing with Golay codes (a), and two STMF methods based on pre-compression (b) and post-compression (c) schemes. The difference between the two STMF images is depicted in (d). It is hard to recognize the difference between the precompressed (Fig. 3b) and post-compressed (Fig. 3c) images. The difference image (Fig. 3d) is normalized to its peak value which is 6.5% of the reference image value (Fig. 3b) at the same position. It shows that the compression error decreases with depth as expected. One can also see that compared to the single-zone focusing method (Fig. 3a) the proposed STMF method provides improved lateral beam patterns except in the vicinity of 30 mm; the
HV Pulser
lateral beam-width and side-lobe levels are much smaller in the near (z 6 20 mm) and far (z P 50 mm) regions. To evaluate the proposed method experimentally, the front-end (FE) board of a commercial ultrasound scanner (SA-9900, Medison Corp., Korea) is modified to fire Golay codes and to acquire the reflected RF data. Fig. 4 shows the resulting experimental set-up. To be specific, the FE controller generates the trigger signals to transmit modulated orthogonal Golay codes combined with focusing delays that can be controlled with 8 ns resolution (i.e., fik ðtÞ of Eq. (3)) using a conventional high-voltage (HV) pulser [12,22,23]. In this paper, a bi-phase rectangular pulse is used as a modulation function m(t). That is, each bit ‘‘1’’ of the Golay code is represented by a rectangular pulse
FE Controller (FPGA)
SDRAM
8-bit ADC
Receive Beamformer
PC Beamfoming Correlation Echo-processing Scan conversion
T/R SW Pre-Amp /TGC
Commercial ultrasound scanner (Sa9900, Medison Corp.) Curved linear array (C2-5IR) 3.85MHz, 60% 6dB BW , 192-element radius: 40mm, angle: 85.256º
Image display and analysis
Model 539 Multipurpose Phantom (ATS laboratori es)
Fig. 4. Experimental set-up to evaluate the proposed method using rf data samples acquired from a commercial ultrasound scanner.
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consisting of a positive high-voltage (Vp) for half the period of the center imaging frequency (i.e., for T/2 = 1/2 f0) followed by a negative high-voltage (Vp) for another T/2 duration, and each bit ‘‘1’’ is represented by a rectangular pulse with the opposite polarity. The highest Vp and the length of sequences that can be transmitted are 60 V and 1 to 512, respectively. The received signals are sampled at a rate of fS = 61.6 MHz with an 8-bit ADC on each of 64 active channels. The resulting samples are fed to the receive beamformers and stored in the SDRAM at the same time. The stored RF data samples are transferred to an external computer in which receive beamforming, pulse compression, and all other back-end signal processing tasks are performed to compare various imaging methods. The receive beamforming is performed at 61.6 MHz by a software model for the conventional delay-sum beamformer using a 4-fold interpolator. The pulse compression is also performed at 61.6 MHz by correlating the RF samples (in the pre-compression scheme) or the focused samples (in the post-compression scheme) with the modulated Golay codes. Note that compared to the conventional pulse-echo imaging the proposed method has an additional computational load to perform pulse compression based on Eqs. (5a) and (5b). Since fS/f0 = 16 and the modulated Golay sequences are also two-level sequences of 1 0 a and 1 0 s, it takes over two T/R cycles 4 · 16 · L 2 0 s complement additions per each input data interval (1/fS) to perform the four correlation operations in addition to the two pair-wise
summations of the correlation sequences. Consequently, the computational overhead of the proposed method is to calculate (4 · 16 · L + 2)/2 = 32L + 1 additions on average per each input data interval. This implies that when L = 16, the proposed method can be implemented by adding a simple hardware to compute 513 additions for each imaging point to the conventional ultrasound imaging system using short pulses. In all experiments, a curved linear array transducer with a center frequency 3.85 MHz and 60% 6 dB bandwidth is used and the smallest f-number is chosen to be 2, because the RSLL for this f-number turned out to be smaller than the noise level of the images obtained with the pre-compression scheme. The number of scan lines and the maximum number of active channels are assumed to be 192 and 64, respectively. Fig. 5 shows B-scan images of a tissue-mimicking phantom (Model 539 Multipurpose Phantom, ATS Laboratories Inc., USA) by the single zone transmit focusing methods based on pre-compression (a) and post-compression (b). For each transmit focal depth, both the compression schemes provide almost the same images. The post-compression image for transmit focus at 4 cm shows much improved near-field spatial resolution than the pre-compression image for transmit focus at 9 cm. These results indicate that the proposed post-compression STMF can improve both the near-field and farfield resolution. Fig. 6 shows B-scan images of the tissue-mimicking phantom by the conventional pulse-echo imaging method
Fig. 5. B-scan images of a tissue-mimicking phantom by the pulse compression method using Golay codes based on: (a) pre-compression and (b) postcompression, when a single transmit focus is fixed at 4 cm (upper panels) and at 9 cm (lower panels).
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Fig. 6. A-scan data (left) and B-scan images (right, dynamic range: 60 dB) of a tissue-mimicking phantom by: (a) the conventional imaging method with a fixed transmit focus at 6 cm, which uses a short pulse of duration 0.27ls with a peak voltage of 20 Vpp, (b) pre-compression based Golay code imaging with a single transmit focus at 6 cm, and (c) the proposed post-compression based STMF method with two transmit foci at 4 cm and 9 cm. Both (b) and (c) are obtained using Golay codes of length 16 (i.e., of duration 4.2 ls) with a peak voltage (20 Vpp).
(a) using a conventional on-off short pulse of duration 0.27 ls, the pre-compression based single-zone transmit focusing method (b), and the proposed post-compression STMF method (c). The transmit focus for the first and second methods is fixed at 6 cm, while the proposed one has two transmit focal points at 4 cm and 9 cm. In both the pre-compression and post-compression schemes, the length of Golay codes is chosen to be 16 (i.e., of duration 4.2 ls). All the waveforms are transmitted with a low peak voltage of 20 Vpp to investigate the advantage of the proposed
method in SNR and other experiment conditions are same as for Fig. 6. For quantitative comparison of SNR, Amode signal along the center of each image is displayed on the left side of the corresponding image. Note that the PSNR measured (from the A-mode signal) for the wire target at 14 cm is 4.2 dB in Fig. 6a, 19 dB in Fig. 6b, and 27 dB in Fig. 6c. That is, the difference in SNR between the pulse-echo imaging and pre-compression based Golay code imaging is 14.8 dB. This 14.8 dB SNR improvement agrees well with the theoretical value, which
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is 10 log10 2L, when the length of Golay codes is L times that of the short pulse [12], L being 16 in this case. The proposed method increases SNR by 8 dB which is due to the 2nd transmit focus at 9 cm whereas the single transmit focus of the pre-compression scheme is at 6 cm. As a result, the post-compression based STMF method (c) shows the cysts with various sizes and wire targets much more clearly around 9 cm and at farther depths. Note that the wire targets appear to have narrow widths in the far field. The advantage of the proposed method can also be confirmed by the measurement result that contrast-to-noise ratio (CNR) of the cyst at 10 cm is 3.02 in Fig. 6b and 5.43 in c. Finally, it should be noticed that the near-field image of the proposed method does not show any sign of degradation of spatial resolution. 4. Conclusion A post-compression based simultaneous transmit multizone focusing method is proposed and verified experimentally. Both the theoretical analysis and beam simulation results confirm that post-compression introduces compression error increasing with decreasing f-number. The proposed post-compression STMF method can reduce the degradation of spatial resolution (due to f-number limitation) in the near field by focusing the ultrasound waves at two depths simultaneously. The experimental results show that the proposed method can improve spatial resolution and SNR in the far field compared to both pulse echo imaging and pre-compression based Golay code imaging. Acknowledgement This work was partially supported by BK21 program and MOST Grant. References [1] M. O’Donnell, Coded excitation system for improving the penetration of real-time phased array imaging systems, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 39 (1992) 341–351. [2] J. Shen, E.S. Ebbini, A new coded-excitation ultrasound imaging system-Part I: basic principles, IEEE Trans. Ultrason. Ferroelect. Freq. Control 43 (1996) 131–140. [3] B. Haider, P.A. Lewin, K.E. Thomenius, Pulse elongation and deconvolution filtering for medical ultrasound imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Control 45 (1998) 98–112. [4] Y. Takeuchi, An investigation of a spread energy method for medical ultrasound systems, Ultrasonics 17 (1979) 219–224. [5] T.X. Misaridis, K. Gammelmark, C.H. Jorgensen, N. Lindberg, A.H. Thomsen, M.H. Pedersen, J.A. Jensen, Potential of coded excitation in medical ultrasound imaging, Ultrasonics 38 (2000) 183–189. [6] M. O’Donnell, Y. Wang, Coded excitation for synthetic aperture ultrasound imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 52 (2005) 171–176.
[7] T. Azuma, Y. Miwa, S. Umemura, Subaperture decoding to enhance performance of coded excitation, IEEE Ultrason. Symp. (2002) 1669– 1672. [8] M.J.E. Golay, Complementary series, IRE Trans. Inform. Theor. IT7 (1961) 82–87. [9] R.Y. Chiao, X.H. Hao, Coded excitation for diagnostic ultrasound: a system developer’s prospective, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 52 (2005) 160–170. [10] A. Nowicki, Z. Klimonda, M. Lewandowski, J. Litniewski, P.A. Lewin, I. Trots, Comparison of sound fields generated by different coded excitations – experimental results, Ultrasonics 44 (2006) 121– 129. [11] T. Misaridis, J.A. Jensen, Use of modulated excitation signals in medical ultrasound. Part II: design and performance for medical imaging applications, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 52 (2005) 192–207. [12] Y.M. Yoo, W.Y. Lee, T.K. Song, A low voltage portable system using a modified golay sequences, IEEE Ultrason. Symp. (2001) 1469–1472. [13] R.Y. Chiao, L.J. Thomas, Synthetic aperture imaging with orthogonal Golay coded excitation, IEEE Ultrason. Symp. (2000) 1677– 1680. [14] R.Y. Chiao, L.J. Thomas, Method and apparatus for ultrasonic beamforming using orthogonal complementary sets, US Patent 6,113,545, Sep. 5, 2000. [15] N.D. Jong, P.J. A Frinking, A. Bouakaz, F.J.T. Cate, Detection procedures of ultrasound contrast agents, Ultrasonics 38 (2000) 87– 92. [16] J.M.G. Borsboom, C.T. Chin, N.D. Jong, Nonlinear coded excitation for ultrasound contrast agent, Ultrasound Med. Biol. 29 (2003) 277– 284. [17] B.A. Schrope, V.L. Newhouse, Second harmonic ultrasonic blood perfusion measurement, Ultrasound Med. Biol. 19 (1993) 567–579. [18] Y. Yakeuchi, Coded excitation for harmonic imaging, IEEE Ultrason. Symp. (1996) 1433–1436. [19] S. Zhou, J.A. Hossack, Dynamic-transmit focusing using timedependent focal zone and center frequency, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 50 (2003) 142–152. [20] H. Peng, X.M. Han, J.Y. Lu, Study on application of complementary Golay code into high-frame rate ultrasonic imaging system, Ultrasonics 44 (2006) e93–e96. [21] M.H. Bae, W.Y. Lee, M.K. Jeong, S.J. Kwon, Orthogonal Golay code based ultrasonic imaging without reducing frame rate, IEEE Ultrason. Symp. (2002) 1705–1708. [22] J.S. Hwang, T.K. Song, Ultrasound imaging apparatus and method using Golay codes with orthogonal property, US Patent No. 6,547,733, 2003. [23] B.H. Kim, W.Y. Lee, T.K. Song, Multiple transmit focusing using modified orthogonal Golay codes for small scale systems, IEEE Ultrason. Symp. (2003) 1574–1577. [24] C.C. Tseng, C.L. Liu, Complementary sets of sequences, IEEE Trans. Inform. Theory IT-18 (1972) 644–652. [25] C.C. Tseng, Signal multiplexing in surface-wave delay lines using orthogonal pairs of Golay’s complementary sequences, IEEE Trans. Sonics Ultrason. SU-18 (1971) 103–107. [26] Y. Takeuchi, An investigation of a spread energy method for medical ultrasound systems. Part One: Theory and investigation, Ultrasonics 17 (1979) 175–182. [27] Y.M. Yoo, T.K. Song, Ultrasound imaging method and apparatus based on pulse compression technique using modified Golay codes, US Patent No. 6,350,240, 2002. [28] J.A. Jensen, Field: A program for simulating ultrasound systems, Med. Biol. Eng. Comput. 34 (1996) 351–353.
A post-compression based ultrasound imaging technique for simultaneous transmit multi-zone focusing Bae-Hyung Kim, Gi-Duck Kim 1, Tai-Kyong Song
*
Department of Electronic Engineering, Sogang University, C.P.O. Box 1142, Seoul 110-611, Republic of Korea Received 27 November 2006; received in revised form 17 January 2007; accepted 19 January 2007 Available online 12 February 2007
Abstract The compression error of post-compression based coded excitation techniques increases with decreasing f-number, which causes the elevation of side-lobe levels. In this paper, a post-compression based coded excitation technique with reduced compression errors through dynamic aperture control is proposed. To improve the near-field resolution with no frame rate reduction, the proposed method performs simultaneous transmit multi-zone focusing using two mutually orthogonal complementary Golay codes. In the proposed method, the two mutually orthogonal sequences of length 16 are simultaneously transmitted toward two different focal depths, which are separately compressed into two short pulses on receive after dynamic focusing is performed. After carrying out the same transmit-receive operation for the same scan line with the complementary set of the orthogonal Golay codes, a single scan line with two transmit foci is obtained.The computer simulation results using a linear array with a center frequency of 7.5 MHz and 60% 6 dB bandwidth show that the range side-lobe level can be suppressed below 50 dB, when f-number is maintained not smaller than 3. The performance of the proposed scheme for a smaller f-number of 2 was also verified through actual experiments using a 3.85 MHz curved linear array with 60% 6 dB bandwidth. Both the simulation and experimental results show that the proposed method provides improved lateral resolution compared to the conventional pre-compressed and post-compression based coded excitation imaging using Golay codes. 2007 Elsevier B.V. All rights reserved. Keywords: Ultrasound Imaging; Coded excitation; Simultaneous; Post-compression; Golay codes
1. Introduction Conventional ultrasound pulse-echo imaging systems have limitations on transmitted energy due to peak power constraints for avoiding tissue damage. Hence, the conventional ultrasound imaging using short transmit pulses often suffer from low signal-to-noise-ratio (SNR) and small detection range. On the other hand, coded excitation, which employs pulse compression techniques, can improve the SNR of ultrasound imaging by increasing average power without affecting instantaneous peak power [1–5]. In coded ultrasound imaging, coded waveforms of a long
*
1
Corresponding author. Tel.: +82 2 705 8907; fax: +82 2 707 3008. E-mail address: [email protected] (T.-K. Song). Co-first author.
0041-624X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2007.01.007
duration are transmitted and the reflected signals are sampled and compressed into a high-amplitude short pulse. Ideally, pulse compression should be performed on the received signal samples on each channel prior to receive beamforming, which is called pre-compression [6,7]. This requires a pulse compressor per each channel, resulting in huge increase in system complexity. Therefore, post-compression, which performs pulse compression on focused RF data, is a very attractive approach, because it only requires a single compression hardware for the whole system. However, post-compression introduces compression error and accompanying degradation in spatial resolution since it is equivalent to performing pulse compression on the irregularly rearranged version (according to the dynamic focusing delay) of the received signal samples on each channel and summing up the resulting compressed signals for all channels.
B.-H. Kim et al. / Ultrasonics 46 (2007) 148–154
Among many coded signals, Golay codes have very attractive properties for medical ultrasound imaging since they consist of a pair of complementary sequences of 1 0 s and 1 0 s and sum of their autocorrelation functions is an impulse function [8]: they can be transmitted with a conventional bi-phase, high-voltage pulser, instead of a more expensive and larger linear power amplifier with low power efficiency, and the received signals can be converted into a short pulse with a high-peak and low range side-lobes using a correlator consisting only of 2 0 s complementary adders [9–12]. For these reasons, the Golay code pulse compression has found various applications in medical ultrasound imaging such as for improving SNR and penetration depth [1–5], spatial resolution based on synthetic aperture techniques with reduced motion artifact [6,13,14], performance of harmonic imaging with and without contrast agents [15– 18], and for reducing the system size [12]. A disadvantage of coded excitation imaging with Golay codes is that it requires two consecutive transmissions to obtain each scan line [10–12]. The resulting frame rate reduction will be harmful particularly when multiple transmit focusing, a conventional method to improve lateral resolution, is employed because it requires the same number of transmit-receive events as the number of transmit focal zones along each scan line [19]. To prevent the frame rate reduction, various imaging methods using orthogonal Golay codes have been studied [13,20–23]. Recently, the authors have suggested pre-compression based coded imaging techniques for simultaneous transmit multi-zone focusing (STMF) [12,22,23]. These methods can achieve multiple transmit focusing without sacrificing the imaging frame rate by transmitting the orthogonal Golay codes focused at different focal depths simultaneously, which can be separated and individually focused on receive using their orthogonal properties [22–25]. However, the pre-compression based coded excitation system using orthogonal Golay codes is not suitable for hand-held or small portable ultrasound systems, because it requires a correlator for each active channel to compress the received signals. This paper suggests a method for improving the spatial resolution by employing the post-compression based STMF using orthogonal Golay codes with reduced compression error. The following section starts with the investigation of an error introduced in post-compression scheme and describes the proposed post-compression based STMF method. The computer simulation and experimental results in Section 3 show the difference between pre- and post-compression schemes. Some conclusions are drawn in the last section.
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the time delay sn with respect to the depth z, which can be expressed as 2 3 " pffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 2 2 osn o z z þ xn 16 1 7 ¼ ¼ 41 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5 oz c c oz 2 1 þ ðxn =zÞ " # 1 1 z 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fn ¼ ¼ ; ð1Þ c 2xn 1 þ 1=4fn2 where c is the velocity of ultrasound and fn is the f-number for the nth element. It is worth noting that the range derivative of the value sn gets smaller for a larger f-number. Since the f-number is proportional to the depth and inversely proportional to xn, the compression error will be the highest for the outer-most element at the nearest depth. Fig. 1 shows the range sidelobe levels (RSLL) of the compressed waveforms for different f-numbers. It is obtained by performing post-compression on the dynamically focused signals from a target at 1 cm when Golay codes of length 2.2 ls are transmitted toward a transmit focus at 1 cm from a 7.5 MHz linear array with element spacing of 0.2 mm. One can see that the compression error leads to increase in RSLL, which decreases with increasing f-number. Therefore, the f-number must be kept larger than a proper value to suppress the compression error below a desired level. For example, to keep the RSLL below 50 dB in Fig. 1, the f-number should not be smaller than 3. Now it becomes obvious that the post-compression based ultrasound beamforming cannot avoid the degradation of spatial resolution due to the f-number limitation. In practice, the f-number starts decreasing from a certain depth, where the number of active elements, which increases with depth, reaches to the pre-determined maximum value. Hence, the problem of limited f-number in post-compression based beamforming will be dominant in the near field.
2. Post-compression based STMF imaging method using orthogonal Golay codes Post-compression introduces errors when dynamic receive focusing is employed [2,9,26]. The amount of the error depends on how fast the delay profile for dynamic focusing changes. Specifically, the compression error for the nth element at xn increases with the rate of change of
Fig. 1. Compressed waveforms of Golay codes of duration 2.2 ls for various f-numbers when post-compression is employed. A 7.5 MHz linear array with element spacing of 0.2 mm is used to transmit the Golay codes toward a point target located at the transmit focus (F = 1 cm).
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N
Correlator A1 Correlator A2 Correlator B1 Correlator B2
TGC N Beamformer /ADC
Zone blending
1st Tx: Orthogonal Golay codes (A1, B1) N pulser
transducer
modulation m(t)
Tx delay controller 2nd Tx: Complementary set of the Orthogonal Golay codes (A2, B2)
Fig. 2. System block diagram to implement the proposed method.
Fig. 2 shows the block diagram of the proposed postcompression based transmit multi-zone focusing method to improve the near-field resolution using two sets of mutually orthogonal Golay sequences of, [A1(n), A2(n)] and [B1(n), B2(n)], which satisfy the followings due to their orthogonal and complementary properties [24,25] ½A1 ðnÞ þ B1 ðnÞ A1 ðnÞ þ ½A2 ðnÞ þ B2 ðnÞ A2 ðnÞ ¼ A1 ðnÞ A1 ðnÞ þ A2 ðnÞ A2 ðnÞ ¼ 2LdðnÞ
ð2aÞ
½A1 ðnÞ þ B1 ðnÞ B1 ðnÞ þ ½A2 ðnÞ þ B2 ðnÞ B2 ðnÞ ¼ B1 ðnÞ B1 ðnÞ þ B2 ðnÞ B2 ðnÞ ¼ 2LdðnÞ
ð2bÞ
where L is the length of Golay codes and represents the relative time duration of the transmitted signal compared to that of a conventional on-off signal. In the first transmit-receive (T/R) event, A1(n) and B1(n) are added together with delays s(F1) and s(F2) for two different focal points F1 and F2, respectively. The combined code is then modulated by a proper function m(t) to be matched to the passband of the imaging transducer [12,27] before being transmitted simultaneously. On receive, the returned signals are dynamically focused and then correlated with each of the modulated codes. The same T/R event is repeated along the same scan line with A2(n) and B2(n). The transmitted signals from the kth array element can be represented as L1 X fAi ðnÞdðt sk ðF 1 Þ nT Þ fik ðtÞ ¼ mðtÞ n¼0
þ Bi ðnÞdðt sk ðF 2 Þ nT Þg;
i ¼ 1; 2
ð3Þ
where L represents the code length, T = 1/f0, and the transducer response is ignored for the convenience of analysis. If we consider the case where two point targets are located at the two transmit foci, the output of receive beamformer can be expressed approximately as ri ðtÞ ¼ mðtÞ
L1 X i ðnÞdðt sðF 1 Þ nT Þ fA n¼0
i ðnÞdðt sðF 2 Þ nT Þg; þB
i ¼ 1; 2
ð4Þ
i ðnÞ and B i ðnÞ represent the dynamically focused sewhere A quences, and s(Fi) denotes the propagation delay from the array center to each transmit focus. Now that the modulated
PL1 signals are givenP by mi;A ðtÞ ¼ mðtÞ n¼0 Ai ðnÞdðt nT Þ and L1 mi;B ðtÞ ¼ mðtÞ n¼0 Bi ðnÞdðt nT Þ, the two correlators in Fig. 2 produce ri(n)*m1 (n) and ri(n)*m2(n) in each T/R cycles. Now, lets assume that the compression error resulting from dynamic focusing in the post-compression scheme can be neglected due to the proper f-number control. Then, it is easy to show that two focused beams along the same scan line are obtained by using the orthogonal and complementary properties of Eqs. (2a) and (2b) as follows: r1 ðtÞ m1;A ðtÞ þ r2 ðtÞ m2;A ðtÞ 2L mðt sðF 1 ÞÞ mðtÞ r1 ðtÞ m1;B ðtÞ þ r2 ðtÞ m2;B ðtÞ
ð5aÞ
2L mðt sðF 2 ÞÞ mðtÞ
ð5bÞ
Finally, by combining the two beams based on the conventional beam blending method, a scan line with two transmit foci is obtained. Consequently, a frame of image with improved resolution is obtained at the same frame rate as that of the conventional pre-compression based single-zone transmit focusing method using Golay codes. It should be noticed that compared to the pre-compression method the proposed post-compression method can save 2(N 1) correlators, where N represents the number of active channels. 3. Experimental results To evaluate the performance of the proposed STMF method based on post-compression, experiments with computer generated signals and actual data acquired from a commercial ultrasound scanner are performed. In all experiments, Golay codes of length 16 generated by using the method in [24,27] are used. In the computer simulation study using Field II [28], a linear array with the center frequency of 7.5 MHz and element pitch of 0.2 mm is used, and the number of scan lines and the maximum number of active channels are assumed to be 192 and 64, respectively. The first transmit focus is set to 20 mm for a near zone up to 38 mm and the second to 50 mm. Since the minimum f-number is chosen to be 3, 64 elements are used from the depth 38 mm. Fig. 3 shows the computer generated B-scan images (dynamic range: 60 dB) of several point
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Fig. 3. Computer generated point target images by various methods: (a) pulse-echo imaging with a single transmit focus at 3 cm, (b) pre-compression based STMF with two transmit foci at 2 cm and 5 cm, (c) post-compression based STMF with transmit foci at 2 cm and 5 cm, and (d) difference between the two images (b) and (c).
targets by using the conventional single zone transmit focusing with Golay codes (a), and two STMF methods based on pre-compression (b) and post-compression (c) schemes. The difference between the two STMF images is depicted in (d). It is hard to recognize the difference between the precompressed (Fig. 3b) and post-compressed (Fig. 3c) images. The difference image (Fig. 3d) is normalized to its peak value which is 6.5% of the reference image value (Fig. 3b) at the same position. It shows that the compression error decreases with depth as expected. One can also see that compared to the single-zone focusing method (Fig. 3a) the proposed STMF method provides improved lateral beam patterns except in the vicinity of 30 mm; the
HV Pulser
lateral beam-width and side-lobe levels are much smaller in the near (z 6 20 mm) and far (z P 50 mm) regions. To evaluate the proposed method experimentally, the front-end (FE) board of a commercial ultrasound scanner (SA-9900, Medison Corp., Korea) is modified to fire Golay codes and to acquire the reflected RF data. Fig. 4 shows the resulting experimental set-up. To be specific, the FE controller generates the trigger signals to transmit modulated orthogonal Golay codes combined with focusing delays that can be controlled with 8 ns resolution (i.e., fik ðtÞ of Eq. (3)) using a conventional high-voltage (HV) pulser [12,22,23]. In this paper, a bi-phase rectangular pulse is used as a modulation function m(t). That is, each bit ‘‘1’’ of the Golay code is represented by a rectangular pulse
FE Controller (FPGA)
SDRAM
8-bit ADC
Receive Beamformer
PC Beamfoming Correlation Echo-processing Scan conversion
T/R SW Pre-Amp /TGC
Commercial ultrasound scanner (Sa9900, Medison Corp.) Curved linear array (C2-5IR) 3.85MHz, 60% 6dB BW , 192-element radius: 40mm, angle: 85.256º
Image display and analysis
Model 539 Multipurpose Phantom (ATS laboratori es)
Fig. 4. Experimental set-up to evaluate the proposed method using rf data samples acquired from a commercial ultrasound scanner.
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consisting of a positive high-voltage (Vp) for half the period of the center imaging frequency (i.e., for T/2 = 1/2 f0) followed by a negative high-voltage (Vp) for another T/2 duration, and each bit ‘‘1’’ is represented by a rectangular pulse with the opposite polarity. The highest Vp and the length of sequences that can be transmitted are 60 V and 1 to 512, respectively. The received signals are sampled at a rate of fS = 61.6 MHz with an 8-bit ADC on each of 64 active channels. The resulting samples are fed to the receive beamformers and stored in the SDRAM at the same time. The stored RF data samples are transferred to an external computer in which receive beamforming, pulse compression, and all other back-end signal processing tasks are performed to compare various imaging methods. The receive beamforming is performed at 61.6 MHz by a software model for the conventional delay-sum beamformer using a 4-fold interpolator. The pulse compression is also performed at 61.6 MHz by correlating the RF samples (in the pre-compression scheme) or the focused samples (in the post-compression scheme) with the modulated Golay codes. Note that compared to the conventional pulse-echo imaging the proposed method has an additional computational load to perform pulse compression based on Eqs. (5a) and (5b). Since fS/f0 = 16 and the modulated Golay sequences are also two-level sequences of 1 0 a and 1 0 s, it takes over two T/R cycles 4 · 16 · L 2 0 s complement additions per each input data interval (1/fS) to perform the four correlation operations in addition to the two pair-wise
summations of the correlation sequences. Consequently, the computational overhead of the proposed method is to calculate (4 · 16 · L + 2)/2 = 32L + 1 additions on average per each input data interval. This implies that when L = 16, the proposed method can be implemented by adding a simple hardware to compute 513 additions for each imaging point to the conventional ultrasound imaging system using short pulses. In all experiments, a curved linear array transducer with a center frequency 3.85 MHz and 60% 6 dB bandwidth is used and the smallest f-number is chosen to be 2, because the RSLL for this f-number turned out to be smaller than the noise level of the images obtained with the pre-compression scheme. The number of scan lines and the maximum number of active channels are assumed to be 192 and 64, respectively. Fig. 5 shows B-scan images of a tissue-mimicking phantom (Model 539 Multipurpose Phantom, ATS Laboratories Inc., USA) by the single zone transmit focusing methods based on pre-compression (a) and post-compression (b). For each transmit focal depth, both the compression schemes provide almost the same images. The post-compression image for transmit focus at 4 cm shows much improved near-field spatial resolution than the pre-compression image for transmit focus at 9 cm. These results indicate that the proposed post-compression STMF can improve both the near-field and farfield resolution. Fig. 6 shows B-scan images of the tissue-mimicking phantom by the conventional pulse-echo imaging method
Fig. 5. B-scan images of a tissue-mimicking phantom by the pulse compression method using Golay codes based on: (a) pre-compression and (b) postcompression, when a single transmit focus is fixed at 4 cm (upper panels) and at 9 cm (lower panels).
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Fig. 6. A-scan data (left) and B-scan images (right, dynamic range: 60 dB) of a tissue-mimicking phantom by: (a) the conventional imaging method with a fixed transmit focus at 6 cm, which uses a short pulse of duration 0.27ls with a peak voltage of 20 Vpp, (b) pre-compression based Golay code imaging with a single transmit focus at 6 cm, and (c) the proposed post-compression based STMF method with two transmit foci at 4 cm and 9 cm. Both (b) and (c) are obtained using Golay codes of length 16 (i.e., of duration 4.2 ls) with a peak voltage (20 Vpp).
(a) using a conventional on-off short pulse of duration 0.27 ls, the pre-compression based single-zone transmit focusing method (b), and the proposed post-compression STMF method (c). The transmit focus for the first and second methods is fixed at 6 cm, while the proposed one has two transmit focal points at 4 cm and 9 cm. In both the pre-compression and post-compression schemes, the length of Golay codes is chosen to be 16 (i.e., of duration 4.2 ls). All the waveforms are transmitted with a low peak voltage of 20 Vpp to investigate the advantage of the proposed
method in SNR and other experiment conditions are same as for Fig. 6. For quantitative comparison of SNR, Amode signal along the center of each image is displayed on the left side of the corresponding image. Note that the PSNR measured (from the A-mode signal) for the wire target at 14 cm is 4.2 dB in Fig. 6a, 19 dB in Fig. 6b, and 27 dB in Fig. 6c. That is, the difference in SNR between the pulse-echo imaging and pre-compression based Golay code imaging is 14.8 dB. This 14.8 dB SNR improvement agrees well with the theoretical value, which
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is 10 log10 2L, when the length of Golay codes is L times that of the short pulse [12], L being 16 in this case. The proposed method increases SNR by 8 dB which is due to the 2nd transmit focus at 9 cm whereas the single transmit focus of the pre-compression scheme is at 6 cm. As a result, the post-compression based STMF method (c) shows the cysts with various sizes and wire targets much more clearly around 9 cm and at farther depths. Note that the wire targets appear to have narrow widths in the far field. The advantage of the proposed method can also be confirmed by the measurement result that contrast-to-noise ratio (CNR) of the cyst at 10 cm is 3.02 in Fig. 6b and 5.43 in c. Finally, it should be noticed that the near-field image of the proposed method does not show any sign of degradation of spatial resolution. 4. Conclusion A post-compression based simultaneous transmit multizone focusing method is proposed and verified experimentally. Both the theoretical analysis and beam simulation results confirm that post-compression introduces compression error increasing with decreasing f-number. The proposed post-compression STMF method can reduce the degradation of spatial resolution (due to f-number limitation) in the near field by focusing the ultrasound waves at two depths simultaneously. The experimental results show that the proposed method can improve spatial resolution and SNR in the far field compared to both pulse echo imaging and pre-compression based Golay code imaging. Acknowledgement This work was partially supported by BK21 program and MOST Grant. References [1] M. O’Donnell, Coded excitation system for improving the penetration of real-time phased array imaging systems, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 39 (1992) 341–351. [2] J. Shen, E.S. Ebbini, A new coded-excitation ultrasound imaging system-Part I: basic principles, IEEE Trans. Ultrason. Ferroelect. Freq. Control 43 (1996) 131–140. [3] B. Haider, P.A. Lewin, K.E. Thomenius, Pulse elongation and deconvolution filtering for medical ultrasound imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Control 45 (1998) 98–112. [4] Y. Takeuchi, An investigation of a spread energy method for medical ultrasound systems, Ultrasonics 17 (1979) 219–224. [5] T.X. Misaridis, K. Gammelmark, C.H. Jorgensen, N. Lindberg, A.H. Thomsen, M.H. Pedersen, J.A. Jensen, Potential of coded excitation in medical ultrasound imaging, Ultrasonics 38 (2000) 183–189. [6] M. O’Donnell, Y. Wang, Coded excitation for synthetic aperture ultrasound imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 52 (2005) 171–176.
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