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Communication Dans Un Congrès Année : 2012

Sparse Binary Matrices of LDPC codes for Compressed Sensing

Résumé

Compressed sensing shows that one undetermined measurement matrix can losslessly compress sparse signals if this matrix satisfies Restricted Isometry Property (RIP). However, in practice there are still no explicit approaches to construct such matrices. Gaussian matrices and Fourier matrices are first proved satisfying RIP with high probabilities. Recently, sparse random binary matrices with lower computation load also expose comparable performance with Gaussian matrices. But they are all constructed randomly, and unstable in orthogonality. In this paper, inspired by these observations, we propose to construct structured sparse binary matrices which are stable in orthogonality. The solution lies in the algorithms that construct parity-check matrices of low-density parity-check (LDPC) codes. Experiments verify that proposed matrices significantly outperform aforementioned three types of matrices. And significantly, for this type of matrices with a given size, the optimal matrix for compressed sensing can be approximated and constructed according to some rules.
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Dates et versions

hal-00659236 , version 1 (12-01-2012)

Identifiants

  • HAL Id : hal-00659236 , version 1

Citer

Weizhi Lu, Kidiyo Kpalma, Joseph Ronsin. Sparse Binary Matrices of LDPC codes for Compressed Sensing. Data Compression Conference (DCC), Apr 2012, Snowbird (Utah), United States. 10 p. ⟨hal-00659236⟩
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