A New Compressed Sensing Algorithm Design Based on Wavelet Frame and Dictionary

Compressed sensing has been paid a lot of attention for its contribution for image restoration, image reconstruction and image representation. Two most common research orientations are the basic theory research and the application research respec- tively. A novel design for compressed sensing frame based on the wavelet frame and dictionary is proposed in this paper. It belongs to the basic theory research and the good performance in the experiments show its efficiency.

[1]  Richard G. Baraniuk,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[2]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[3]  Gabriel Peyré.  Best basis compressed sensing , 2010, IEEE Trans. Signal Process..

[4]  Chih-Hung Lin,et al.  Reversible Data Hiding for High-Quality Images Based on Integer Wavelet Transform , 2012, J. Inf. Hiding Multim. Signal Process..

[5]  Hsiang-Cheh Huang,et al.  Watermarking for Compressive Sampling Applications , 2012, 2012 Eighth International Conference on Intelligent Information Hiding and Multimedia Signal Processing.

[6]  Constantinos Patsakis,et al.  LSB and DCT steganographic detection using compressive sensing , 2014, J. Inf. Hiding Multim. Signal Process..

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

[8]  Wei Li,et al.  Data Hiding Based on Subsampling and Compressive Sensing , 2013, 2013 Ninth International Conference on Intelligent Information Hiding and Multimedia Signal Processing.

[9]  S. Shankar Sastry,et al.  Generalized principal component analysis (GPCA) , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[11]  Kjersti Engan,et al.  Recursive Least Squares Dictionary Learning Algorithm , 2010, IEEE Transactions on Signal Processing.

[12]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[13]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[14]  Pierre Vandergheynst,et al.  Compressed Sensing and Redundant Dictionaries , 2007, IEEE Transactions on Information Theory.

[15]  Guillermo Sapiro,et al.  Online Learning for Matrix Factorization and Sparse Coding , 2009, J. Mach. Learn. Res..

[16]  Beiji Zou,et al.  Optimal Approach for Texture Analysis and Classification based on Wavelet Transform and Neural Network , 2011, J. Inf. Hiding Multim. Signal Process..

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

[18]  Lei Liu,et al.  Adaptive Distributed Compressed Video Sensing , 2014, J. Inf. Hiding Multim. Signal Process..

[19]  Bu-Sung Lee,et al.  Robust image compression based on compressive sensing , 2010, 2010 IEEE International Conference on Multimedia and Expo.

[20]  Rémi Gribonval,et al.  Learning unions of orthonormal bases with thresholded singular value decomposition , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[21]  Levent Sendur,et al.  A bivariate shrinkage function for wavelet-based denoising , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  E.J. Candes.  Compressive Sampling , 2022 .

[23]  Emmanuel J. Cand.  The Restricted Isometry Property and Its Implications for Compressed Sensing , 2008 .

[24]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[25]  Volkan Cevher,et al.  Model-Based Compressive Sensing , 2008, IEEE Transactions on Information Theory.