Compressive sensing for noisy video reconstruction

In this paper, a compressing and reconstruction method for a noise video based on Compressed Sensing (CS) theory is proposed. At first, the CS theory is presented. Then the noise video is estimated from noisy measurement by solving the convex minimization problem. The video recovery algorithms based on gradient-based method is used to compressing and reconstructing the noise signal. And a compressive sensing algorithm with gradient-based method is proposed. At last, the performance of the proposed approach is shown and compared with some conventional algorithms. Our method can obtain best results in terms of peak signal noise ratio (PSNR) than those achieved by common methods with only a little runtime.

[1]  Mohammed Ghanbari,et al.  Scope of validity of PSNR in image/video quality assessment , 2008 .

[2]  M. Lustig,et al.  Improved pediatric MR imaging with compressed sensing. , 2010, Radiology.

[3]  I. Daubechies,et al.  Iteratively reweighted least squares minimization for sparse recovery , 2008, 0807.0575.

[4]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[5]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.

[6]  Andreas Antoniou,et al.  A new algorithm for compressive sensing based on total-variation norm , 2013, 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013).

[7]  Steven W. Zucker,et al.  Greedy Basis Pursuit , 2007, IEEE Transactions on Signal Processing.

[8]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[9]  Emil Y. Sidky,et al.  Quantifying Admissible Undersampling for Sparsity-Exploiting Iterative Image Reconstruction in X-Ray CT , 2011, IEEE Transactions on Medical Imaging.

[10]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[11]  T. Blumensath,et al.  Fast Encoding of Synthetic Aperture Radar Raw Data using Compressed Sensing , 2007, 2007 IEEE/SP 14th Workshop on Statistical Signal Processing.

[12]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[13]  Jean-Luc Starck,et al.  Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit , 2012, IEEE Transactions on Information Theory.

[14]  Lie Wang,et al.  Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise , 2011, IEEE Transactions on Information Theory.

[15]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[16]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[17]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[18]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .