Bipartite Graph based Construction of Compressed Sensing Matrices

This paper proposes an efficient method to construct the bipartite graph with as many edges as possible while without introducing the shortest cycles of length equal to 4. The binary matrix associated with the bipartite graph described above presents comparable and even better phase transitions than Gaussian random matrices.

[1]  Andrea Montanari,et al.  Message-passing algorithms for compressed sensing , 2009, Proceedings of the National Academy of Sciences.

[2]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[3]  Marc E. Pfetsch,et al.  The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing , 2012, IEEE Transactions on Information Theory.

[4]  Farrokh Marvasti,et al.  Deterministic Construction of Binary, Bipolar, and Ternary Compressed Sensing Matrices , 2009, IEEE Transactions on Information Theory.

[5]  Shu-Tao Xia,et al.  Constructions of quasi-cyclic measurement matrices based on array codes , 2013, 2013 IEEE International Symposium on Information Theory.

[6]  Jacques Verstraëte,et al.  A Note on Bipartite Graphs Without 2k-Cycles , 2005, Combinatorics, Probability and Computing.

[7]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[8]  David L. Donoho,et al.  Precise Undersampling Theorems , 2010, Proceedings of the IEEE.

[9]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[10]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[11]  Ronald A. DeVore,et al.  Deterministic constructions of compressed sensing matrices , 2007, J. Complex..

[12]  A. Robert Calderbank,et al.  Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property , 2009, IEEE Journal of Selected Topics in Signal Processing.

[13]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

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