Image Reconstruction Algorithm for Electrical Capacitance Tomography Based on Sparsity Adaptive Compressed Sensing
WU Xinjie① YAN Shiyu① XU Panfeng① YAN Hua②
①(College of Physics, Liaoning University, Shenyang 110036, China) ②(School of Information Science and Engineering, Shenyang University of Technology, Shenyang 110870, China)
Abstract：In order to improve quality of the reconstructed images of the Electrical Capacitance Tomography (ECT) system, an improved sparsity adaptive matching pursuit compressed sensing algorithm is proposed. Based on the coherence point of Compressed Sensing (CS) theory and ECT, the CS-ECT model is established. In the model, the sensitivity matrix of ECT is designed in a random order to be the observation matrix, the discrete cosine base is used as the sparse base, the capacitance value is measured as the observed value. By using the Linear Back Projection (LBP) algorithm, the sparsity of the estimated images is confirmed. The sparsity can be served as the initial value of the atomic index for sparsity adaptive iteration. The lack of image reconstruction accuracy caused by the inaccurate estimate of sparsity can be solved by the improved sparsity adaptive matching pursuit algorithm. Simulation results indicate that reconstructed images with higher accuracy can be obtained using the improved sparsity adaptive matching pursuit compressed sensing algorithm than the LBP algorithm, Landweber algorithm and Tikhonov algorithm. A new method of ECT reconstruction is provided.
WU Xinjie, HE Zaigang, LI Huiqiang, et al. Image reconstruction by using multi-criteria of hopfield network for ECT[J]. Electric Machines and Control, 2016, 20(8): 98-104. doi: 10.15938/j.emc.2016.08.013.
ZHANG Lifeng, LIU Zhaolin, and TIAN Pei. Image reconstruction algorithm for electrical capacitance tomography based on compressed sensing[J]. Acta Electronica Sinica, 2017, 45(2): 353-358. doi: 10.3969/j.issn. 0372-2112.2017.02.013.
[4]
DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306. doi: 10.1109/ TIT.2006.871582.
[5]
TSAIG Y and DONOHO D L. Extensions of compressed sensing[J]. Signal Processing, 2006, 86(3): 549-571. doi: 10.1016/j.sigpro.2005.05.029.
[6]
METZLER C A, MALEKI A, and BARANIUK R G. From denoising to compressed sensing[J]. IEEE Transactions on Information Theory, 2016, 62(9): 5117-5144. doi: 10.1109/ TIT.2016.2556683.
[7]
BIGOT J, BOYER C, and WEISS P. An analysis of block sampling strategies in compressed sensing[J]. IEEE Transactions on Information Theory, 2016, 62(4): 2125-2139. doi: 10.1109/TIT.2016.2524628.
[8]
ROMBERG J. Imaging via compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2): 14-20. doi: 10.1109/ MSP.2007.914729.
YAN Tao, CHEN Jianwen, and BAO Zheng. Sea clutter suppression method for over-the-horizon radar with short coherent integration time based on compressed sensing [J]. Journal of Electronics & Information Technology, 2017, 39(4): 945-952. doi: 10.11999/JEIT160576.
CHENG Yinbo, SI Jingjing, and HOU Xiaolan. Hierarchical distributed compressed sensing for wireless sensor network [J]. Journal of Electronics & Information Technology, 2017, 39(3): 539-545. doi: 10.11999/JEIT160439.
[11]
FRACASTORO G, FOSSON S M, and MAGLI E. Steerable discrete cosine transform[J]. IEEE Transactions on Image Processing, 2017, 26(1): 303-314. doi: 10.1109/TIP.2016. 2623489.
[12]
RAMAKRISHNAN A G, ABHIRAM B, and MAHADEVA P S R. Voice source characterization using pitch synchronous discrete cosine transform for speaker identification[J]. The Journal of the Acoustical Society of America, 2015, 137(6): EL469-EL475. doi: 10.1121/1.4921679.
[13]
MESSAOUDI A and SRAIRI K. Colour image compression algorithm based on the DCT transform using difference lookup table[J]. Electronics Letters, 2016, 52(20): 1685-1686. doi: 10.1049/el.2016.2115.
[14]
CANDES E J, ROMBERG J, and TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509. doi: 10.1109/TIT.2005.862083.
[15]
CANDES E J, ROMBERG J, and TAO T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics, 2006, 59(8): 1207-1223. doi: 10.1002/cpa.20124.
[16]
CANDES E J and TAO T. Decoding by linear programming [J]. IEEE Transactions on Information Theory, 2005, 51(12): 4203-4215. doi: 10.1109/TIT.2005.858979.
[17]
NATARAJAN B K. Sparse approximate solutions to linear systems[J]. SIAM Journal on Computing, 1995, 24(2): 227-234. doi: 10.1137/S0097539792240406.
[18]
CHEN S S, DONOHO D L, and SAUNDERS M A. Atomic decomposition by basis pursuit[J]. SIAM Review, 2001, 43(1): 129-159. doi: 10.1137/S003614450037906X.
[19]
TROPP J A and GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666. doi: 10.1109/TIT.2007.909108.
[20]
NEEDELL D and VERSHYNIN R. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit[J]. Foundations of Computational Mathematics, 2009, 9(3): 317-334. doi: 10.1007/s10208-008- 9031-3.
[21]
THONG T D, LU Gan, NAM Nguyen, et al. Sparsity adaptive matching pursuit algorithm for practical compressed sensing[C]. 2008 42nd Asilomar Conference on Signals Systems and Computers, Pacific Grove, CA, USA, 2008, 10: 581-587.
WU Xinjie, HUANG Guoxing, and WANG Jingwen. Application of compressed sensing to flow pattern identification of ECT[J]. Optics and Precision Engineering, 2013, 21(4): 1062-1068. doi: 10.3788/OPE.20132104.1062.
