- Email: [email protected]
Noise reduction in selective computational ghost imaging using genetic algorithm
Optics Communications 387 (2017) 182–187
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Noise reduction in selective computational ghost imaging using genetic algorithm
crossmark
⁎
Mohammad Zafari, Sohrab Ahmadi-Kandjani , Reza Kheradmand Photonics Group, Research Institute for Applied Physics and Astronomy, University of Tabriz, Tabriz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Selective computational ghost imaging Genetic algorithm Modification method Background-free ghost image Universal image quality index
Recently, we have presented a selective computational ghost imaging (SCGI) method as an advanced technique for enhancing the security level of the encrypted ghost images. In this paper, we propose a modified method to improve the ghost image quality reconstructed by SCGI technique. The method is based on background subtraction using genetic algorithm (GA) which eliminates background noise and gives background-free ghost images. Analyzing the universal image quality index by using experimental data proves the advantage of this modification method. In particular, the calculated value of the image quality index for modified SCGI over 4225 realization shows an 11 times improvement with respect to SCGI technique. This improvement is 20 times in comparison to conventional CGI technique.
1. Introduction Ghost imaging (GI) is a novel correlated-photon imaging technique. The most considerable advantage of this method is non-requirement of putting the object in front of the imaging sensors. Common GI method follows using two highly correlated optical beams; one beam interacts with an object and then collected by a single-pixel output detector, termed the bucket detector. Another beam instead of striking the object impinges on a high-resolution (multiple-pixel) detector mostly a kind of imaging sensors like: Charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS). The cross-correlation between two optical beams results ghost image [1–10]. Ghost imaging is performed originally by using orthogonally polarized idler and signal beams produced by spontaneous parametric down conversion (SPDC) process [11]. Subsequent theory and experiments demonstrated in GI, consideration of quantum viewpoint and photon's entanglement are not mandatory. Thus, the GI can be performed with a classical (thermal or pseudo-thermal) light source by considering the classical light correlation [12–14]. In traditional GI with thermal light, a spatially incoherent beam, which is produced by linear propagation of laser light through rotating ground-glass, is separated to the signal and reference arms. It has been shown that computational ghost imaging is easier and has higher speed operation than other configurations [15,16]. By implementing a spatial light modulator (SLM) to generate a random pattern, in computational ghost imaging (CGI), we can easily replace the reference arm with numerical computations and there is no need for the beam splitter and a multiple-pixel detector. Recently the 3D
⁎
form of CGI has performed that uses several single-pixel detectors in different locations [17]. The most considerable difference between quantum ghost imaging and classical ghost imaging is the matter of visibility. The biphoton ghost image can achieve 100% visibility, but there is a background level or noise in pseudo-thermal ghost image [18]. Many different techniques have been proposed to overcome this limitation and improve pseudo-thermal ghost image quality [19–24] (e.g. compressive GI, differential GI and normalized GI). Compressive GI [19] uses an algorithm based on compressed sensing that reduces the number of realizations required for ghost image reconstruction. The imaging of weakly absorbing objects is possible by differential GI [20] and measuring the transmission function of an object in absolute units. In normalized GI [21], a normalized weighting algorithm is used to improve image quality. Recently, we have introduced selective computational ghost imaging (SCGI) as a new technique which enables the reconstruction of an N-pixel image from N measurements or less [25]; this technique has a great advantage on optical encryption. In this paper, we propose a novel method to modify and improve image quality reconstructed by SCGI technique that we name it “modified selective computational ghost imaging (MSCGI)”. In addition to the conventional methods for improving ghost image quality, in this work, we used a genetic algorithm as an optimization method to reduce background noise in SCGI. To evaluate the performance of MSCGI, we analyzed a new image quality parameter namely the universal image quality index.
Corresponding author. E-mail address: [email protected] (S. Ahmadi-Kandjani).
http://dx.doi.org/10.1016/j.optcom.2016.11.064 Received 6 September 2016; Received in revised form 21 November 2016; Accepted 23 November 2016 0030-4018/ © 2016 Elsevier B.V. All rights reserved.
Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 1. Genetic algorithm flowchart. Fig. 4. Calculated quality index in each iteration by genetic algorithm.
SLM, but one arbitrary element of it attributes to a different value that is much larger than others in a way that the transmitted intensity from this element will be much greater than the other elements [25]. Since in each realization one and only one element of the matrix attributes to a different value, in the total iterations, each element takes a different value just once. Accordingly, the maximum realization required for reconstructing images with the best quality is equal to multiplying the matrix's number of rows and columns; in other words, N is equal to the size of I (x, y ). Thus, SCGI has the capability of reconstructing an Npixel image from M measurements where M⩽N.
Fig. 2. Experimental setup of computational ghost imaging.
2. Selective computational ghost imaging (SCGI)
3. Genetic algorithm (GA)
In CGI by computing cross-correlation between known intensity pattern at the object plane, Ii = Ei (x, y, z = L ) 2 , and measured intensities of bucket detector Bi = ∫ dxdyIi (x, y, L ) T (x, y ), ghost image can be retrieved:
G (x , y ) =
1 N
Genetic algorithm (GA), which is known as a random optimization method, was invented by John Holland in the 1970s [26]. GA is based on Darwin's theory of gradual evolution. For developing the solutions of an optimization problem, the algorithm uses the same principles that nature implement on the evolution of gene symbols [27–30]. A common method used to implement the genetic algorithm is as the following:
N
∑ (Bi − 〈B〉) Ii (x, y) = 〈BI (x, y)〉 − 〈B〉〈I (x, y)〉 i =1
(1)
In conventional computational ghost imaging (CCGI), speckle patterns applied to the SLM in the form of random matrices. So, each array of the matrix attributes to one random value as an intensity modulator. Consequently, in every realization, each matrix array will be a random value. Similarly, in SCGI method, in each realization, we consider a random matrix as an intensity modulator to establish on the
• •
A set of random solutions, which are called populations, are generated. In each iteration, all solutions are evaluated using a fitness function. Then, some of the best solutions are selected using a probability
Fig. 3. Experimentally reconstructed ghost images with size 65×65 pixel from 4225 realization. (a) Original slide (b) CCGI (c) MCCGI (d) SCGI and (e) MSCGI.
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Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 5. Plot of normalized intensity derived from the photodetected signal. (a) CCGI, (b) MCCGI, (c) SCGI and (d) MSCGI.
• •
distortion in ghost image reconstructed with SCGI technique [Figs. 3, 5]. In the proposed method for MSCGI, a background subtraction process is applied in order to eliminate the background noise and obtain background-free ghost images. As we can see in SCGI intensity plot [Fig. 5-c], there is a background noise causing low image quality. But, we have overcome this limitation in MSCGI. As a matter of fact, to diminish the existing noise in the system using genetic algorithm, following process is conducted: I) a set of arbitrary intensities are chosen as a threshold noise limit (Initial population); II) By reducing the intensities lower than the threshold noise limit, ghost images of object are reconstructed and the image quality index of each image is calculated (Evaluation); III) Image quality indexes are compared. If the stop criterion of the algorithm satisfies, the process will stop. Otherwise, some of the threshold noise limits, which lead to higher image quality index, are selected to constitute a new population (Satisfy stop criterion). IV) New population is constitute using these selected threshold noise limits and also by applying GA operators (New population); V) The process is continued to find the specific threshold noise limit that leads to the highest image quality index. It should be noted that if the same image quality index obtains in four consecutive iterations, the process will stop which is considered as the stop criterion. It should be mentioned that CCGI is not compatible with our proposed method and by applying this noise reduction process to CCGI, the image quality will be decreased. As it is shown in Fig. 6, in the case of MCCGI, intensity distribution in image plane is distorted.
function and constitute a new population. Some of these selected solutions are used without changing and others using genetic operators such as Crossover and Mutation are used to generate offspring. The process is continued to find the optimal solution. The Genetic algorithm flowchart is shown in Fig. 1.
4. Results and discussions To demonstrate the performance of SCGI, experimentally, we used a He-Ne laser with the wavelength of λ = 632.8nm and beam waist of ω0 = 498μm impinging on a SLM [Fig. 2]. The maximum resolution of the SLM plane is 130×130 pixels with a pixel size of 209 µm ×209 µm. In each realization, a 65×65 pixels random pattern loaded on the SLM; therefore, we consider each 2×2 SLM pixels as a unit. Simulated pseudo-thermal light using loaded random patterns on the SLM, leaving the SLM meet the 28 mm×28 mm object plane at a distance of L=52 cm from the SLM plane. Using a normal imaging sensor such as CMOS of size 640×480pixels (4 mm×3 mm) located at the distance of 16 cm from the object plane, it is possible to detect intensity fluctuations in each measurement. To determine the transverse resolution, we used the van Cittert–Zernike theorem δx = λz / πω0 [5] that in our experiment it is δx (52cm ) = 209μm . Reconstructing the ghost image of a “plus mark” and according to the normalized intensities derived from the photodetected signal, it can be seen that there is a level of background noise which has caused a 184
Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 6. Three dimensional plot of intensity distribution in image plane (x and y show pixels position). (a) CCGI (b) MCCGI (c) SCGI and (d) MSCGI.
To compare the advantages of MSCGI with SCGI and CCGI method, the universal image quality index (Q ) was calculated. To calculate the quality index, we use the definition used by Wang & Bavik [31,32]. By definition of the x = {xi |i = 1, 2, ..., N} as the original image signal and y = {yi |i = 1, 2, ..., N} as the test image signal, respectively; the universal image quality index is defined as:
Q=
4σxy x y (σx2 + σy2 )[(x )2 + (y )2 ]
(2)
where
x =
1 N
N
∑ xi , y i =1
1 σy2 = N−1
Fig. 7. Comparison between the quality index of CCGI, MCCGI, SCGI and MSCGI.
N
∑ i =1
=
1 N
N
∑ yi σx2 = i =1
1 N−1
1 (yi − y )2 σxy = N−1
N
∑ (x i − x ) 2 , i =1 N
∑ (xi − x )(yi − y ) i =1
The lowest and the highest value of Q is −1 and 1 which denotes the worst and the best compatibility of the original and test image signal, respectively. Superiority of the universal image quality index is that it can be represent any distortion as a combination of loss of correlation, luminance distortion and variance distortion [31,32]. To compute quality index of natural images, the sliding window approach with a window size of B×B (normally 8×8) is used. In each step, related window of original and test image converted into a vector as an image signal and quality index is computed for each window. Averaging computed quality index of all steps results the overall image quality index of the image:
The reason is that in SCGI in each iteration the focus is on a particular pixel and when this pixel is scanned in dark areas of the object, the intensities that is recorded by a bucket detector is also low and it is known as a background noise. Thus, by decreasing the intensities lower than a threshold noise limit to zero, the background noise of the system is reduced. But in CCGI, the intensities recorded by a bucket detector in each iteration include comprehensive information about the whole object. Thus, at the case of CCGI, by decreasing the intensities lower than a threshold noise limit to zero, indeed information about the whole object is reduced and this causes the distortion in the recovered image. 185
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M. Zafari et al.
Fig. 8. Reconstructed images from 1500 (top) and 2000 (down) realization. (a) CCGI. (b) SCGI and (c) MSCGI.
Fig. 9. Schematic diagram of setting different values sequentially to the columns of matrix.
Fig. 10. Reconstructed images from: (a) 1:1820, (b) 1820:2210, (c) 2210:2600 and (d) 2600:4225 realization by setting random values sequentially to the columns of matrix from top to bottom and left to right.
Q=
1 M
M
between CCGI and SCGI; in CCGI, the image quality is reduced by the reduction of the realization while in SCGI the number of reconstructed points of the object is reduced by the reduction of the realization which is an advantage in optical encryption based on ghost imaging [25]. Also, in SCGI by using two (1×2 pixels), four (2×2 pixels) or more side by side points with different values in each realization, the number of realizations reduces to 1/2, 1/4 or less, respectively; but the edges of the image will be disturbed [25]. Another exclusive capability of SCGI is the ability of it to retrieve an image separately from the determined parts of an object. This eventuality is provided by choosing certain measurements and setting different values sequentially, and not randomly, to the rows or columns (from first row or column to the final row or column) of matrix in
∑ Qj j =1
(3)
where M is the number of total steps and Qj is the computed local quality index of the j-th step. Fig. 4 shows the calculated quality index in each iteration by genetic algorithm. As it can be seen in Fig. 4, after 15 iterations, the quality index is not changed and it means that GA is converged after 15 iterations, and optimum threshold noise limit is found. Fig. 7 compares Q MSCGI , QSCGI , QCCGI and Q MCCGI that shows striking difference between three methods. As it can be seen in Fig. 7, for low shot numbers, the efficiency of three methods is almost the same, while with increasing the shot number, the MSCGI become more efficient than SCGI, CCGI and MCCGI. As shown in Fig. 8, there is a difference 186
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[9] W. Chen, Correlated-photon secured imaging by iterative phase retrieval using axially-varying distances, IEEE Photonics Technol. Lett. 28 (2016) 1932–1935. [10] W. Chen, Modulating phase via rotation for optical encoding based on correlated photon imaging, IEEE Photonics Technol. Lett. 28 (2016) 540–543. [11] T. Pittman, Y. Shih, D. Strekalov, A. Sergienko, Optical imaging by means of twophoton quantum entanglement, Phys. Rev. A 52 (1995) R3429–R3432. [12] R.S. Bennink, S.J. Bentley, R.W. Boyd, Two-Photon Coincidence Imaging with a Classical Source, Phys. Rev. Lett. 89 (2002) 113601. [13] F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, L. Lugiato, High-resolution ghost image and ghost diffraction experiments with thermal light, Phys. Rev. Lett. 94 (2005) 183602. [14] A. Valencia, G. Scarcelli, M. D'Angelo, Y. Shih, Two-photon imaging with thermal light, Phys. Rev. Lett. 94 (2005) 063601. [15] J.H. Shapiro, Computational ghost imaging, Phys. Rev. A 78 (2008) 061802. [16] Y. Bromberg, O. Katz, Y. Silberberg, Ghost imaging with a single detector, Phys. Rev. A 79 (2009) 053840. [17] B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, M. Padgett, 3D Computational imaging with single-pixel detectors, Science 340 (2013) 844–847. [18] B.I. Erkmen, J.H. Shapiro, Ghost imaging: from quantum to classical to computational, Adv. Opt. Photonics 2 (2010) 405–450. [19] O. Katz, Y. Bromberg, Y. Silberberg, Compressive ghost imaging, Appl. Phys. Lett. 95 (2009) (131110-131110-131113). [20] F. Ferri, D. Magatti, L. Lugiato, A. Gatti, Differential ghost imaging, Phys. Rev. Lett. 104 (2010) 253603. [21] B. Sun, S.S. Welsh, M.P. Edgar, J.H. Shapiro, M.J. Padgett, Normalized ghost imaging, Opt. Express 20 (2012) 16892–16901. [22] W. Wang, Y.P. Wang, J. Li, X. Yang, Y. Wu, Iterative ghost imaging, Opt. Lett. 39 (2014) 5150–5153. [23] X.-R. Yao, W.-K. Yu, X.-F. Liu, L.-Z. Li, M.-F. Li, L.-A. Wu, G.-J. Zhai, Iterative denoising of ghost imaging, Opt. Express 22 (2014) 24268–24275. [24] H. Ghanbari-Ghalehjoughi, S. Ahmadi-Kandjani, M. Eslami, High quality computational ghost imaging using multi-fluorescent screen, J. Opt. Soc. Am. A 32 (2015) 323–328. [25] M. Zafari, R. Kheradmand, S. Ahmadi-Kandjani, Optical encryption with selective computational ghost imaging, J. Opt. 16 (2014) 105405. [26] J.H. Holland, Adaptation in Natural and Artificial Systems: an Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, U Michigan Press, Michigan, 1975. [27] D.E. Golberg, Genetic ALgorithms in Search, Optimization, and Machine Learning, Addion wesley, Boston, 1989. [28] R. Franz, Representations for Genetic and Evolutionary Algorithms in, Springer– Verlag, Berling, Heidelberg, Netherlands, 2006. [29] R.L. Haupt, D.H. Werner, Genetic Algorithms in Electromagnetics, John Wiley & Sons, New Jersey, 2007. [30] R.L. Haupt, S.E. Haupt, Practical Genetic Algorithms, John Wiley & Sons, New Jersey, 2004. [31] Z. Wang, A.C. Bovik, A universal image quality index, IEEE Signal Process. Lett. 9 (2002) 81–84. [32] Z. Wang, A.C. Bovik, L. Lu, Why is image quality assessment so difficult?, IEEE ICASSP Int. Conf. (2002) (pp. IV-3313-IV-3316).
consecutive measurements. In this case, the corresponding part of the object that bright pixel scans according to Fig. 9, will be retrieved and non-scanned part of the object will be lost [Fig. 10]. 5. Conclusion A novel modification method based on background subtraction using genetic algorithm is proposed that improves the quality of ghost image reconstructed by SCGI technique dramatically. This method operates on intensities derived from the photodetected signal to diminish the existing noise in the imaging system. To evaluate the performance of the modification method, a new image quality parameter namely the universal image quality index is computed. Furthermore, it is shown that in SCGI technique, for the first time to the best of our knowledge, by choosing certain measurements we can retrieve an image separately from the determined parts of an object. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] A. Gatti, E. Brambilla, M. Bache, L. Lugiato, Ghost imaging with thermal light: comparing entanglement and classicalcorrelation, Phys. Rev. Lett. 93 (2004) 93602. [2] A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, L. Lugiato, Coherent imaging with pseudo-thermal incoherent light, J. Mod. Opt. 53 (2006) 739–760. [3] B.I. Erkmen, J.H. Shapiro, Unified theory of ghost imaging with Gaussian-state light, Phys. Rev. A 77 (2008) 043809. [4] J.H. Shapiro, R.W. Boyd, The physics of ghost imaging, Quantum Inf. Process. 11 (2012) 949–993. [5] M. Tanha, R. Kheradmand, S. Ahmadi-Kandjani, Gray-scale and color optical encryption based on computational ghost imaging, Appl. Phys. Lett. 101 (2012) 101108. [6] M. Tanha, S. Ahmadi-Kandjani, R. Kheradmand, H. Ghanbari, Computational fluorescence ghost imaging, Eur. Phys. J. D 67 (2013) 1–4. [7] M. Tanha, S. Ahmadi-Kandjani, R. Kheradmand, Fast ghost imaging and ghost encryption based on the discrete cosine transform, Phys. Scr. Vol. T 157 (2013) 4059. [8] W. Chen, X. Chen, Grayscale object authentication based on ghost imaging using binary signals, Europhys. Lett. 110 (2015) 44002.
187
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Noise reduction in selective computational ghost imaging using genetic algorithm
crossmark
⁎
Mohammad Zafari, Sohrab Ahmadi-Kandjani , Reza Kheradmand Photonics Group, Research Institute for Applied Physics and Astronomy, University of Tabriz, Tabriz, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Selective computational ghost imaging Genetic algorithm Modification method Background-free ghost image Universal image quality index
Recently, we have presented a selective computational ghost imaging (SCGI) method as an advanced technique for enhancing the security level of the encrypted ghost images. In this paper, we propose a modified method to improve the ghost image quality reconstructed by SCGI technique. The method is based on background subtraction using genetic algorithm (GA) which eliminates background noise and gives background-free ghost images. Analyzing the universal image quality index by using experimental data proves the advantage of this modification method. In particular, the calculated value of the image quality index for modified SCGI over 4225 realization shows an 11 times improvement with respect to SCGI technique. This improvement is 20 times in comparison to conventional CGI technique.
1. Introduction Ghost imaging (GI) is a novel correlated-photon imaging technique. The most considerable advantage of this method is non-requirement of putting the object in front of the imaging sensors. Common GI method follows using two highly correlated optical beams; one beam interacts with an object and then collected by a single-pixel output detector, termed the bucket detector. Another beam instead of striking the object impinges on a high-resolution (multiple-pixel) detector mostly a kind of imaging sensors like: Charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS). The cross-correlation between two optical beams results ghost image [1–10]. Ghost imaging is performed originally by using orthogonally polarized idler and signal beams produced by spontaneous parametric down conversion (SPDC) process [11]. Subsequent theory and experiments demonstrated in GI, consideration of quantum viewpoint and photon's entanglement are not mandatory. Thus, the GI can be performed with a classical (thermal or pseudo-thermal) light source by considering the classical light correlation [12–14]. In traditional GI with thermal light, a spatially incoherent beam, which is produced by linear propagation of laser light through rotating ground-glass, is separated to the signal and reference arms. It has been shown that computational ghost imaging is easier and has higher speed operation than other configurations [15,16]. By implementing a spatial light modulator (SLM) to generate a random pattern, in computational ghost imaging (CGI), we can easily replace the reference arm with numerical computations and there is no need for the beam splitter and a multiple-pixel detector. Recently the 3D
⁎
form of CGI has performed that uses several single-pixel detectors in different locations [17]. The most considerable difference between quantum ghost imaging and classical ghost imaging is the matter of visibility. The biphoton ghost image can achieve 100% visibility, but there is a background level or noise in pseudo-thermal ghost image [18]. Many different techniques have been proposed to overcome this limitation and improve pseudo-thermal ghost image quality [19–24] (e.g. compressive GI, differential GI and normalized GI). Compressive GI [19] uses an algorithm based on compressed sensing that reduces the number of realizations required for ghost image reconstruction. The imaging of weakly absorbing objects is possible by differential GI [20] and measuring the transmission function of an object in absolute units. In normalized GI [21], a normalized weighting algorithm is used to improve image quality. Recently, we have introduced selective computational ghost imaging (SCGI) as a new technique which enables the reconstruction of an N-pixel image from N measurements or less [25]; this technique has a great advantage on optical encryption. In this paper, we propose a novel method to modify and improve image quality reconstructed by SCGI technique that we name it “modified selective computational ghost imaging (MSCGI)”. In addition to the conventional methods for improving ghost image quality, in this work, we used a genetic algorithm as an optimization method to reduce background noise in SCGI. To evaluate the performance of MSCGI, we analyzed a new image quality parameter namely the universal image quality index.
Corresponding author. E-mail address: [email protected] (S. Ahmadi-Kandjani).
http://dx.doi.org/10.1016/j.optcom.2016.11.064 Received 6 September 2016; Received in revised form 21 November 2016; Accepted 23 November 2016 0030-4018/ © 2016 Elsevier B.V. All rights reserved.
Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 1. Genetic algorithm flowchart. Fig. 4. Calculated quality index in each iteration by genetic algorithm.
SLM, but one arbitrary element of it attributes to a different value that is much larger than others in a way that the transmitted intensity from this element will be much greater than the other elements [25]. Since in each realization one and only one element of the matrix attributes to a different value, in the total iterations, each element takes a different value just once. Accordingly, the maximum realization required for reconstructing images with the best quality is equal to multiplying the matrix's number of rows and columns; in other words, N is equal to the size of I (x, y ). Thus, SCGI has the capability of reconstructing an Npixel image from M measurements where M⩽N.
Fig. 2. Experimental setup of computational ghost imaging.
2. Selective computational ghost imaging (SCGI)
3. Genetic algorithm (GA)
In CGI by computing cross-correlation between known intensity pattern at the object plane, Ii = Ei (x, y, z = L ) 2 , and measured intensities of bucket detector Bi = ∫ dxdyIi (x, y, L ) T (x, y ), ghost image can be retrieved:
G (x , y ) =
1 N
Genetic algorithm (GA), which is known as a random optimization method, was invented by John Holland in the 1970s [26]. GA is based on Darwin's theory of gradual evolution. For developing the solutions of an optimization problem, the algorithm uses the same principles that nature implement on the evolution of gene symbols [27–30]. A common method used to implement the genetic algorithm is as the following:
N
∑ (Bi − 〈B〉) Ii (x, y) = 〈BI (x, y)〉 − 〈B〉〈I (x, y)〉 i =1
(1)
In conventional computational ghost imaging (CCGI), speckle patterns applied to the SLM in the form of random matrices. So, each array of the matrix attributes to one random value as an intensity modulator. Consequently, in every realization, each matrix array will be a random value. Similarly, in SCGI method, in each realization, we consider a random matrix as an intensity modulator to establish on the
• •
A set of random solutions, which are called populations, are generated. In each iteration, all solutions are evaluated using a fitness function. Then, some of the best solutions are selected using a probability
Fig. 3. Experimentally reconstructed ghost images with size 65×65 pixel from 4225 realization. (a) Original slide (b) CCGI (c) MCCGI (d) SCGI and (e) MSCGI.
183
Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 5. Plot of normalized intensity derived from the photodetected signal. (a) CCGI, (b) MCCGI, (c) SCGI and (d) MSCGI.
• •
distortion in ghost image reconstructed with SCGI technique [Figs. 3, 5]. In the proposed method for MSCGI, a background subtraction process is applied in order to eliminate the background noise and obtain background-free ghost images. As we can see in SCGI intensity plot [Fig. 5-c], there is a background noise causing low image quality. But, we have overcome this limitation in MSCGI. As a matter of fact, to diminish the existing noise in the system using genetic algorithm, following process is conducted: I) a set of arbitrary intensities are chosen as a threshold noise limit (Initial population); II) By reducing the intensities lower than the threshold noise limit, ghost images of object are reconstructed and the image quality index of each image is calculated (Evaluation); III) Image quality indexes are compared. If the stop criterion of the algorithm satisfies, the process will stop. Otherwise, some of the threshold noise limits, which lead to higher image quality index, are selected to constitute a new population (Satisfy stop criterion). IV) New population is constitute using these selected threshold noise limits and also by applying GA operators (New population); V) The process is continued to find the specific threshold noise limit that leads to the highest image quality index. It should be noted that if the same image quality index obtains in four consecutive iterations, the process will stop which is considered as the stop criterion. It should be mentioned that CCGI is not compatible with our proposed method and by applying this noise reduction process to CCGI, the image quality will be decreased. As it is shown in Fig. 6, in the case of MCCGI, intensity distribution in image plane is distorted.
function and constitute a new population. Some of these selected solutions are used without changing and others using genetic operators such as Crossover and Mutation are used to generate offspring. The process is continued to find the optimal solution. The Genetic algorithm flowchart is shown in Fig. 1.
4. Results and discussions To demonstrate the performance of SCGI, experimentally, we used a He-Ne laser with the wavelength of λ = 632.8nm and beam waist of ω0 = 498μm impinging on a SLM [Fig. 2]. The maximum resolution of the SLM plane is 130×130 pixels with a pixel size of 209 µm ×209 µm. In each realization, a 65×65 pixels random pattern loaded on the SLM; therefore, we consider each 2×2 SLM pixels as a unit. Simulated pseudo-thermal light using loaded random patterns on the SLM, leaving the SLM meet the 28 mm×28 mm object plane at a distance of L=52 cm from the SLM plane. Using a normal imaging sensor such as CMOS of size 640×480pixels (4 mm×3 mm) located at the distance of 16 cm from the object plane, it is possible to detect intensity fluctuations in each measurement. To determine the transverse resolution, we used the van Cittert–Zernike theorem δx = λz / πω0 [5] that in our experiment it is δx (52cm ) = 209μm . Reconstructing the ghost image of a “plus mark” and according to the normalized intensities derived from the photodetected signal, it can be seen that there is a level of background noise which has caused a 184
Optics Communications 387 (2017) 182–187
M. Zafari et al.
Fig. 6. Three dimensional plot of intensity distribution in image plane (x and y show pixels position). (a) CCGI (b) MCCGI (c) SCGI and (d) MSCGI.
To compare the advantages of MSCGI with SCGI and CCGI method, the universal image quality index (Q ) was calculated. To calculate the quality index, we use the definition used by Wang & Bavik [31,32]. By definition of the x = {xi |i = 1, 2, ..., N} as the original image signal and y = {yi |i = 1, 2, ..., N} as the test image signal, respectively; the universal image quality index is defined as:
Q=
4σxy x y (σx2 + σy2 )[(x )2 + (y )2 ]
(2)
where
x =
1 N
N
∑ xi , y i =1
1 σy2 = N−1
Fig. 7. Comparison between the quality index of CCGI, MCCGI, SCGI and MSCGI.
N
∑ i =1
=
1 N
N
∑ yi σx2 = i =1
1 N−1
1 (yi − y )2 σxy = N−1
N
∑ (x i − x ) 2 , i =1 N
∑ (xi − x )(yi − y ) i =1
The lowest and the highest value of Q is −1 and 1 which denotes the worst and the best compatibility of the original and test image signal, respectively. Superiority of the universal image quality index is that it can be represent any distortion as a combination of loss of correlation, luminance distortion and variance distortion [31,32]. To compute quality index of natural images, the sliding window approach with a window size of B×B (normally 8×8) is used. In each step, related window of original and test image converted into a vector as an image signal and quality index is computed for each window. Averaging computed quality index of all steps results the overall image quality index of the image:
The reason is that in SCGI in each iteration the focus is on a particular pixel and when this pixel is scanned in dark areas of the object, the intensities that is recorded by a bucket detector is also low and it is known as a background noise. Thus, by decreasing the intensities lower than a threshold noise limit to zero, the background noise of the system is reduced. But in CCGI, the intensities recorded by a bucket detector in each iteration include comprehensive information about the whole object. Thus, at the case of CCGI, by decreasing the intensities lower than a threshold noise limit to zero, indeed information about the whole object is reduced and this causes the distortion in the recovered image. 185
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Fig. 8. Reconstructed images from 1500 (top) and 2000 (down) realization. (a) CCGI. (b) SCGI and (c) MSCGI.
Fig. 9. Schematic diagram of setting different values sequentially to the columns of matrix.
Fig. 10. Reconstructed images from: (a) 1:1820, (b) 1820:2210, (c) 2210:2600 and (d) 2600:4225 realization by setting random values sequentially to the columns of matrix from top to bottom and left to right.
Q=
1 M
M
between CCGI and SCGI; in CCGI, the image quality is reduced by the reduction of the realization while in SCGI the number of reconstructed points of the object is reduced by the reduction of the realization which is an advantage in optical encryption based on ghost imaging [25]. Also, in SCGI by using two (1×2 pixels), four (2×2 pixels) or more side by side points with different values in each realization, the number of realizations reduces to 1/2, 1/4 or less, respectively; but the edges of the image will be disturbed [25]. Another exclusive capability of SCGI is the ability of it to retrieve an image separately from the determined parts of an object. This eventuality is provided by choosing certain measurements and setting different values sequentially, and not randomly, to the rows or columns (from first row or column to the final row or column) of matrix in
∑ Qj j =1
(3)
where M is the number of total steps and Qj is the computed local quality index of the j-th step. Fig. 4 shows the calculated quality index in each iteration by genetic algorithm. As it can be seen in Fig. 4, after 15 iterations, the quality index is not changed and it means that GA is converged after 15 iterations, and optimum threshold noise limit is found. Fig. 7 compares Q MSCGI , QSCGI , QCCGI and Q MCCGI that shows striking difference between three methods. As it can be seen in Fig. 7, for low shot numbers, the efficiency of three methods is almost the same, while with increasing the shot number, the MSCGI become more efficient than SCGI, CCGI and MCCGI. As shown in Fig. 8, there is a difference 186
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consecutive measurements. In this case, the corresponding part of the object that bright pixel scans according to Fig. 9, will be retrieved and non-scanned part of the object will be lost [Fig. 10]. 5. Conclusion A novel modification method based on background subtraction using genetic algorithm is proposed that improves the quality of ghost image reconstructed by SCGI technique dramatically. This method operates on intensities derived from the photodetected signal to diminish the existing noise in the imaging system. To evaluate the performance of the modification method, a new image quality parameter namely the universal image quality index is computed. Furthermore, it is shown that in SCGI technique, for the first time to the best of our knowledge, by choosing certain measurements we can retrieve an image separately from the determined parts of an object. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] A. Gatti, E. Brambilla, M. Bache, L. Lugiato, Ghost imaging with thermal light: comparing entanglement and classicalcorrelation, Phys. Rev. Lett. 93 (2004) 93602. [2] A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, L. Lugiato, Coherent imaging with pseudo-thermal incoherent light, J. Mod. Opt. 53 (2006) 739–760. [3] B.I. Erkmen, J.H. Shapiro, Unified theory of ghost imaging with Gaussian-state light, Phys. Rev. A 77 (2008) 043809. [4] J.H. Shapiro, R.W. Boyd, The physics of ghost imaging, Quantum Inf. Process. 11 (2012) 949–993. [5] M. Tanha, R. Kheradmand, S. Ahmadi-Kandjani, Gray-scale and color optical encryption based on computational ghost imaging, Appl. Phys. Lett. 101 (2012) 101108. [6] M. Tanha, S. Ahmadi-Kandjani, R. Kheradmand, H. Ghanbari, Computational fluorescence ghost imaging, Eur. Phys. J. D 67 (2013) 1–4. [7] M. Tanha, S. Ahmadi-Kandjani, R. Kheradmand, Fast ghost imaging and ghost encryption based on the discrete cosine transform, Phys. Scr. Vol. T 157 (2013) 4059. [8] W. Chen, X. Chen, Grayscale object authentication based on ghost imaging using binary signals, Europhys. Lett. 110 (2015) 44002.
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