A new scan conversion algorithm for ultrasound compound scanning

LTRASONIC

IrMAGING

7,

215-224

(1985)

A NEW SCAN CONVERSION ALGORITHM FOR ULTRASOUND COMPOUND SCANNING Seung-Woo Korea

Lee and Song-Bai

Park

Department of Electrical Engineering Advanced Institute of Science and Technology P.O. Box 150, Chongyangni, Seoul, Korea

An improved scan conversion algorithm for ultrasound compound scanning is proposed. In this algorithm, the input data in the spatial domain is sampled by the concentric square raster sampling (CSRS) method, and the display pixel data are filled by one-dimensional linear interpolation. The reconstruction error of the proposed algorithm is much smaller than that of other algorithms, because only one-dimensional, rather than two-dimensional, interpolation is involved. This algorithm greatly simplifies implementation of a real-time digital scan converter (DSC) for spatial compounding of ultrasound images. 0 1985 Academic Press, Inc. Key words:

I.

Compound scanning; one-dimensional digital scan converter; scan sampling.

interpolation; real conversion; variable

time rate

INTRODUCTION

Compound scanning is used to overcome major problems in ultrasound reflectors or B-scan imaging, e.g., the difficulty of imaging specular objects lying behind highly-reflecting or attenuating structures, and the speckle noise. Also, the compound system has a larger field of view, better resolution and better SNR, compared to the single sector or linear scanning system. Moreover, compound scanning increases the image information by its pixel value assignment capability, that is, by selecting a pixel value from the detected peak value, the detected minimum value, the integrated value, or the average value, of the data obtained from different views [1,2]. Some scan conversion techniques for single sector scanning can also be used for compound scanning. In the conventional ultrasound sector scanner, the input data are sampled in the polar coordinates (r,e) (Fig. la) while the display pixel data are located in the Cartesian coordinates conversion process is necessary. (x,Y) (Fig. lb), and hence a coordinate Many conversion methods have been proposed in the past [3-61. simplest conversion The algorithm is the nearest neighbor interpolation algorithm (NNIA) [3], which maps the sampled data in the polar coordinates to the nearest display pixel in the Cartesian coordinates. As a result of this mapping process, the well-known Moire' artifacts appear in the displayed image. One technique for reducing the Moire' pattern is to interpolate radial rays between the actual scan lines. This method still leaves unsampled pixels in the far field and enhances the overwriting problem in the near field, making difficult its 0161-7346/85 215

$3.00

Copyright 0 198.5 by Academic Press, Inc. AN rights of reproduction in any form reserved.

LEE AND PARK

Fig.

1

a Sampling coordinates vs. display coordinates. (b) Cartesian (x,y)

b

coordinates. coordinates.

(a)

Polar

(r,R)

implementation for real-time applications. The postprocessing interpolation is a relatively simple technique to eliminate the Moire' artifacts, which has been successfully used in ultrasound imaging. However, since the postprocessing is done for the display pixel, which is obtained by NNIA, the displayed image is degraded. Another method of filling the unsampled pixels between the sampled scan lines is to use a nonlinear smoothing algorithm. In this technique, unsampled pixels are filled with the average value of eight neighbor pixels except zero-valued pixels [4]. Then, the resulting image has no unsampled pixels, but it blurs due to the smearing effect. In addition, this technique requires pixel address calculation and an average logic, making real-time difficult. implementation The two-dimensional linear interpolation which algorithm, was proposed in [5,6] and implemented for a real-time sector scan converter [6], does provide a high quality image with very sophisticated circuitry. However, even this algorithm does not completely eliminate the interpolation error and the resolution error in the radial and the To eliminate lateral directions [7]. the above-mentioned artifacts, the uniform ladder algorithm (ULA) was proposed [8]. Since this algorithm basically eliminates the coordinate conversion process (and hence the interpolation process), the reconstruction error can be almost completely removed. above-mentioned algorithms are applied to a real-time When the spatial compound scan converter, their characteristics remain the same but the pixel value assignment capability may not be implemented efficiently in real-time because of the necessity of elimination of unfilled pixels, which requires either an increased number of scan lines The or hardware complexity in the cases of the NNIA and fill-in methods. in two-dimensional linear interpolation requires even more complexity implementation [6]. The ULA may be most suitable for the compound system in figure t3S well, when the transducers are arranged linearly as shown 2a. In that case, the same DSC can be used for all transducer arrays with to account a proper initial delay introduced to the respective arrays there are several problems for their different positions. However, inherent to the linear arrangement of transducers. One is the difficulty of good contact with the round human body, and the other is reduced improvement in the resolution in the compounded area and in the specular reflector detection. A more desirable arrangement may be the circular one as depicted in figure 2b, for which, however, the ULA cannot be applied of the directly and the same DSC's cannot be used any more because different positions and orientations of the arrays.

216

SCAN CONVERSION FOR COMPOUND SCAN

b

0

Fig.

II.

2

Transducer arrangement.

arrangement.

(a)

Linear

arrangement.

(b)

Circular

SCAN CONVERSION ALGORITHM

one-dimensional linear In this section, we will discuss a interpolation technique based on the concentric square raster sampling (CSRS) proposed by Mersereau and Oppenheim [9]. The CSRS method was developed as a reconstructon algorithm of Direct Fourier Transform (DFT) tomography. Its original concept is illustrated in figure 3a, where the frequency sampling interval is varied depending on the angle of each view. This represents equal angle sampling between two adjacent views. In this case, the sampling density becomes sparse toward the 45" and 135" directions. As an alternative method, equal interval sampling is shown in figure 3b. In this paper, we propose a new scan conversion algorithm compound scanning based on the CSRS. The CSRS seems more suitable ultrasound imaging, since variable rate sampling is performed in spatial domain rather than in the frequency domain originally intended the CSRS.

for for the by

Since. the sample points in the CSRS are distributed symetrically about the lines 8 = 0", 45', 90" and 135', it suffices to specify the design parameters (the scan angle and the sampling interval) for 0"<8<45" only. In the equal angle case, the i-th scan angle is given by 0(i)

=

n/2N

(i-l),

i = 1, 2, . . . . N/2 + 1,

(1)

--x -

//I

I\\\\

b

0

Fig.

3

(Zonce ntric

square

raster -. (a )Equal

217

angle.

(b)Equa .1 interval,

LEE AND PARK

Y 4

Y i=N

I=N t

1=N/2+1

-

a Fig.

4

and for o(i)

equal

where

T(0)

interval

= tan-l[(i-1)

where N is the sampling interval T(i)

b

Design parameters (b) Equal interval.

the

= T(0)

in proposed

number of scan is given by / cos

algorithm.

e(i), interval

i = 1, 2, lines

Equal

angle.

N/2 + 1,

in one quadrant.

i = 1, 2, for

. ..)

(2)

In both

cases,

. . . . n/2 + 1,

the (3)

ti = 0

d(scan depth at 6 = 0) M(# of samples to be taken along the

d is determined depth, and M is display monitor. the first quadrant.

(a)

case, / (N/Z)],

= sampling =

I=N/2

scan line

0 = 0).

by the transducer characteristics and the penetration determined by the bandwidth of the transducer and the Figure 4 illustrates the aforementioned parameters in

As can be seen in Eq. the proposed algorithm needs variable (3), rate sampling process to replace the one-dimensional interpolation process. In the implementation of the real time system, one requires a variable satisfying the following rate sampling clock generator requirements: very precise frequency ultra fast switching time, resolution, and phase coherency. The switching time is determined by the blanking interval of the sampling rate pulse, and the required frequency resolution depends on the allowable error in the reconstructed image. The starting phase of the sampling clock should be coherent over the entire scan lines. Otherwise, the actual sampling location will differ from the desired location by an amount of the offset value. It is well known in sampling original image may be obtained from dimensional interpolation function.

theory that reconstruction of the its samples using an appropriate twoIn our case, since one coordinate of

218

SCAN CONVERSION FOR COMPOUND SCAN

. : SAMPLE

PIXEL

+ : DISPLAY

PIXEL

? s KJ

Fig.

5

One-dimensional

linear

in terpolation.

the sample space is identical to that of the display space, interpolation one-dimensional sample data to display data involves only from interpolation rather than the complicated two-dimensional interpolation required for the polar raster. Thus, interpolation error in one which is the other direction (vertical or horizontal) is eliminated and that in direction is reduced because they affect each other. The generalized Z(x)

=

one-dimensional

:mS(x-uji Z(Xj), m where Z(x) is the interpolated the actual sample value is interpolation function.

interpolation

formula

is

by (4)

j=-

The ideal reconstruction, sine function, which is infinite in the real time system. interpolation function which The intensity values image. samples are interpolated using

given

value at Xj

at the display and S(.) is

pixel an

site x, Z(xj) one-dimensional

requires interpolation with the of course, in extent and therefore, not realizable Therefore, we choose a simple linear provides a good replica of the original for all pixels lying between two adjacent the equation

Z(x) = Z(xi) + [Z(X~+~) - Uxi)l

AL/L,

(5)

where L = xi+l

- xi and AL = x - x..1

The method of interpolation scan conversion is illustrated in figure 5. Note that the sample interval along any scan line is always equal to, or grid size, and that linear less than, fi a, where a is the square pixel interpolation is performed vertically (horizontally) in the region where sample points are aligned vertically (horizontally). This principal holds also for compound scanning, except that sampling now may not start coherently on every scan line except for one transducer. As can be seen from Eq. (5), this one-dimensional linear interpolation requires only two multiplications and two additions for one interpolation, making it suitable for implementing the real time DSC for compound as well as single sector scanning. III. consists

EXPERIMENTAL

SYSTEM

Figure 6 shows of an Aerotech

the schematic of a compound imaging pulser, the Data 6000 data acquisition

219

system, system and

LEE AND PARK

PULSER (AEROTECH

)

I AMPLIFIER 1 VARIABLE

RATE

GENERATOR MICRO (MING

ENVELOPE DETECTOR I

COMPUTER

I

lf/23) A/D

(DATA

MINI COMPUTER WAX 11/7!30)

7

CONVERTER 6CW)

IMAGE DISPLAY (GRINNEL) 1

Fig.

6

Block

diagram

of the

experimental

system.

the Grinnel display system interfaced with MING 11/23 computer which acts as a controller. The MINC 11/23 computer is also connected with a VAX 11/750 computer for executing various interpolation algorithms. Data is obtained by rotating a piston type transducer in 0.9"steps, which has a fixed focal distance of 5 cm, a center frequency of 2.25 MHz and a bandwidth of 0.9 MHz. The received pulse echo is subjected to rf time gain compensation (TGC), logarithmic amplication, amplification, envelope detection, and then digitization with a variable rate sampling The clock which effectively replaces interpolation in one direction. sampling clock generator must satisfy two requirements: precise frequency resolution and phase coherency. Digitized &bit data is transfered to the VAX 11/750 through the MINC 11/23. One frame is formed by 101 scan lines Various scan conversion algorithms and each scan line has 400 samples. are executed on the VAX 11/750 and the resulting ultrasound images are transfered to the Grinnel image display system through the MING 11123. conventional sector image, the To maintain visual compatibility with the penetration depth is fixed for all scan lines. As a result, the number of samples differs in different scan lines, as shown in figure 4. The number of sampling pixels per scan line increases toward 0" and 90" , whereas it decreases toward 45" and 135'.

220

SCAN CONVERSION FOR COMPOUND SCAN

IV.

RESULTS

In this section, we report performance of compound and single various interpolation techniques.

the experimental sector scans in

results combination

on

the with

In the first experiment, a line reflector was placed at the focal point of the transducer and the beam was directed normal or oblique to the horizontal scan direction. The processed images are shown in figure 7. The top image (A) is obtained with a normal incident beam, the with an oblique incident beam and the bottom (C) is a middle image (B),

Fig.

7

Reconstructed image by various scan (a) NNIA with polar sampling. (b) interpolation with polar sampling. linear interpolation with CSRS. In incident beam, B : Oblique incident three-dimensional image with a normal

221

conversion algorithms. Two-dimensional linear (c) One-dimensional each figure, A : Normal beam, C : Cut view of incident beam.

LEE AND PARK

Fig.

a

8

Three-dimensional plot of reconstructed image. (a) Two-dimensional linear interpolation with polar sampling. (b) Onedimensional linear interpolation with CSRS.

b

cut view of the three-dimensional image obtained with a normal incident beam. All of them manifest the unfilled pixels clearly. In figure 7a, polar sampling and NNIA were used. Figure 7b shows those obtained with polar sampling and two-dimensional linear interpolation. Figure 7c shows those obtained by the proposed techniques; they are smoother and less blocky compared with the previous images with.an~~~~~~q~ep~~~~i~e~~~~~~~~~~~~~ three-dimensional image obtained figure 8a, polar sampling and two-dimensional interpolation were used, while in figure 8b, CSRS and one-dimensional interpolation were used. We see that, compared with the former, the latter has better resolution in the lateral as well as in the axial directions. In the next experiment, a sponge phantom with holes of different sizes was used, which is supposed to consist of numerous random reflectors. The image obtained by compound as well as single sector scans in combination with various interpolation techniques are shown in figure 9. Single sector scanning was used in figures 9a, b and c while compound scanning was used in figure 9d. The bright spot at the upper edge center corresponds to a line reflector. In figure 9a, polar sampling and NNIA were used. In figure 9b, polar sampling and two-dimensional linear interpolation were used. In figure 9c, CSRS and one-dimensional linear interpolation are placed below were used. In figure 9d, two transducers the lower edge of the phantom and faced upward, intersecting at the line reflector at 24". The image was obtained by compounding with average pixel values. We see that this is the best image in figure 9. In order to compare the transducers are arranged resolution by the inverse of by c i e=

resolution quantitatively linearly and circularly, the mean-squared-distance c

when we error

two sector define the as defined

A(i,j)'D(i,j)

j

(6)

i *j where A(i,j) D and sector

(i,,

= [{interpolated - factual ((i-i,)

zz

jo)

2

value +(j-jo)

= the position

The resolution is represented compound scanning. In this

value at (i,j)} at (i,j)}] 2

)

4

of point

reflector

for dual by the height in figure 10, the echo signal was sampled simulation,

222

SCAN CONVERSION FOR COMPOUND SCAN

Fig.

9

Reconstructed image of random reflectors by various scan conversion algorithms. (a)NNIA with polar sampling. (b)Twointerpolation with polar sampling. (c) dimensional linear One-dimensional linear interpolation with CSRS. (d) Dual sector by averge reconstruction technique (each sector is obtained by the proposed algorithm).

Fig.

10

Resolution improvement in dual sector compound image. (a) Circular arrangement 6 = 10'. (b) Circular arrangement 8= 45". (c)Circular arrangement 0 = 90". (d)Linear arrangement.

223

LEE AND PARK

by the CSRS and processed by one-dimensional lOa, b and cb two transducers are arranged on angle of 10 , 45"and 90", respectively. In distinctive levels of height (or resolution). the uncompounded area and the higher level, expected, we see that higher resolution can arrangement of the transducers (in particular, V.

interpolation. In figures an arc with an intersecting these figures, we note two The lower level represents the compounded area. As be obtained by a circular with 90" intersection).

CONCLUSION

The concentric square raster sampling is employed in ultrasound sector scanning with the advantage that one-dimensional only interpolation with variable rate sampling is needed, resulting in improved image quality and simpler real time implementation of the DSC. The technique can be applied to compound as well as single sector scans. For the compound scan system for medical imaging, improved resolution is obtained by a circular, rather than a linear, arrangement of the transducers. All of these facts were verified by actual imaging or computer simulation. Implementation of proposed approach), interpolation methods, scan using the proposed applications have been

the variable rate sampling clock (the key in the error analysis and comparisons of various and experimental results with a complete compound techniques will be reported elsewhere, Patent filed for the techniques.

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and Knight scan pulse-echo

P. C., imaging,

Digital J., and Maklad N. F., imaging, Proc. IEEE 67, 654-664

[4] Robinson D. E, pulse-echo ultrasound,

and Knight Ultrasonic

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Computer Ultrasonic

reconstruction Imaging 3, 217

scan converters (1979). Interpolation 4, 297-310

in diagnostic

scan conversion (1982).

in

Algorithm for Use [5] Larsen H. G., and Leavitt S. C., An Image Display in Real-Time Sector Scanners with Digital Scan Converter, in 1980 IEEE Ultrasonic Symp. Proc., pp. 763-765 (IEEE Cat. No. 80 CH 1602-2SU). [6] Leavitt S. C., algolithm for display (1983).

Hunt B. F., ultrasound

and Larsen H. G., Hewlett-Packard images,

Digital me Processing, [7] Pratt W. K., Wiley & Sons, Los Angeles, CA, 1978).

A scan conversion 30-34 J. 34,

pp. 93-120

Chap.

4 (John

Algorithm for Real[8] Park S. B., and Lee M. H., A New Scan Conversion Time Sector Scanner, in 1984 IEEE U1trasQni.c Svmn. Proc., pp. 723-727 (IEEE Cat. No. 84 CH 2112-l). [9] Mersereau multidimensional (1974).

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