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Comparative Study of Compressive Sensing Techniques For Image Enhancement
Sahar Ujan, Seyed Ghorshi, Majid Pourebrahim
Pages - 106 - 120     |    Revised - 30-06-2017     |    Published - 01-08-2017
Volume - 11   Issue - 4    |    Publication Date - August 2017  Table of Contents
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KEYWORDS
Compressive Sensing, Basis Pursuit (BP), Compressive Sampling Matching Pursuit (CoSaMP), Approximate Message Passing (D-AMP), Non-local Means (NLM), Bayesian Least Squares Gaussian Scale Mixtures (BL, Block Matching 3D collaborative filter (BM3D).
ABSTRACT
Compressive Sensing is a new way of sampling signals at a sub-Nyquist rate. For many signals, this revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. In this work, compressed sensing method is proposed to reduce the noise of the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit de-noising (BPDN) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. Ultimately, it is demonstrated that the proposed methods can't perfectly recover the image signal. Therefore, we have used a complementary approach for enhancing the performance of CS recovery with non-sparse signals. In this work, we have used a new designed CS recovery framework, called De-noising-based Approximate Message Passing (D-AMP). This method uses a de-noising algorithm to recover signals from compressive measurements. For de-noising purpose the Non-Local Means (NLM), Bayesian Least Squares Gaussian Scale Mixtures (BLS-GSM) and Block Matching 3D collaborative have been used. Also, in this work, we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).
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1 E. Candés, J. Emmanuel, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," Information Theory, IEEE Transactions, Vol. 52 (2), pp. 489-509, Feb. 2006.
2 E. Candes, J. Emmanuel and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies," Information Theory, IEEE Transactions, Vol. 52 (12), pp. 5406-5425, Dec. 2006.
3 M. Lustig, D. Donoho, and M. John Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic resonance in medicine, Vol. 58 (6), pp.1182-1195, Oct. 2007.
4 Donoho, L. David, "Compressed sensing, "Information Theory, IEEE Transactions, Vol. 52 (4), pp.1289-1306, Apr. 2006.
5 Baraniuk, G. Richard, E. Candés, R. Nowak, and M. Vetterli, "Compressive sampling," IEEE Signal Processing Magazine, Vol. 25 (2), pp. 12-13, March. 2008.
6 Starck, J. Luc, F. Murtagh, and M.J Fadili, "Sparse image and signal processing: wavelets, curvelets, morphological diversity," Cambridge university press, 2010.
7 P. Breen, "Algorithms for sparse approximation," School of Mathematics, University of Edinburgh, Year 4 project, 2009.
8 M. Elad, "Sparse and Redundant Representation, from theory to applications in signal and image processing", The Technin- Israel Institute of technology, Springer, 2010.
9 H. Yang, "Compressed sensing-with applications to medical imaging," 2011.
10 S. Foucart and R. Holger, "A mathematical introduction to compressive sensing," Springer New York, 2013, pp. 111-131.
11 SS. Chen, L. D. Donoho, and MA. Saunders, "Atomic decomposition by basis pursuit," SIAM journal on scientific computing, Vol. 20 (1), pp. 33-61, 2001.
12 E. Candes, J. Emmanuel, K.J Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Communications on pure and applied mathematics, Vol. 59 (8), pp. 1207-1223, Aug. 2006.
13 D. Needell, and A. Joel Tropp, "CoSaMP: iterative signal recovery from incomplete and inaccurate samples," Communications of the ACM, Vol. 53, no. 12, pp:93-100, May. 2009.
14 S. Satpathi, and M. Chakraborty, "On the number of iterations for convergence of CoSaMP and SP algorithm," arXiv preprint arXiv, pp. 1404.4927, Apr. 2014.
15 B. Zhang, X. Cheng, N. Zhang, Y. Cui, Y. Li, and Q. Liang, "Sparse target counting and localization in sensor networks based on compressive sensing," In INFOCOM, 2011, pp. 2255-2263.
16 A. Buades, B. Coll, and JM Morel, "A non-local algorithm for image denoising," In Computer Vision and Pattern Recognition, IEEE Computer Society Conference, Vol. 2, 2005, pp. 60-65.
17 M. Lebrun, "An Analysis and Implementation of the Bm3d Image Denoising Method," in Image Processing on Line, 2012, pp. 175-213.
18 H. Om, and M. Biswas, "An improved image denoising method based on wavelet thresholding," Journal of Signal and Information Processing, Vol. 3(1), pp. 10.4236, Dec. 2011.
19 CA. Metzler, A. Maleki, and R.G Baraniuk, "From denoising to compress sensing," IEEE Transactions on Information Theory, Vol. 62 (9), pp. 5117-44, Sep. 2016.
20 CA. Metzler, A. Maleki, and R.G Baraniuk, "Optimal Recovery from Compressive Measurements via Denoising-based Approximate Message Passing," In Sampling Theory and Applications, 2015, pp. 508-512.
21 J. Benesty, J. Chen, Y.A Huang, S. Doclo, "Study of the Wiener filter for noise reduction," InSpeech Enhancement Springer Berlin Heidelberg, pp. 9-41, 2005.
22 J. Tan, Y. Ma and D. Baron, "Compressive imaging via approximate message passing with image denoising," IEEE Transactions on Signal Processing, Vol 63(8), pp.2085-2092, 2015.
Miss Sahar Ujan
School of Science & Engineering Sharif University of Technology International Campus, Kish Island, Iran - Iran
Dr. Seyed Ghorshi
School of Science & Engineering Sharif University of Technology International Campus, Kish Island, Iran - Iran
ghorshi@kish.sharif.edu
Mr. Majid Pourebrahim
School of Science & Engineering Sharif University of Technology International Campus, Kish Island, Iran - Iran