Abstract
Compressed Sensing (CS) avails mutual coherence metric to choose the measurement matrix that is incoherent with dictionary matrix. Random measurement matrices are incoherent with any dictionary, but their highly uncertain elements necessitate large storage and make hardware realization difficult. In this paper deterministic matrices are employed which greatly reduce memory space and computational complexity. To avoid the randomness completely, deterministic sub-sampling is done by choosing rows deterministically rather than randomly, so that matrix can be regenerated during reconstruction without storing it. Also matrices are generated by orthonormalization, which makes them highly incoherent with any dictionary basis. Random matrices like Gaussian, Bernoulli, semi-deterministic matrices like Toeplitz, Circulant and full-deterministic matrices like DFT, DCT, FZC-Circulant are compared. DFT matrix is found to be effective in terms of recovery error and recovery time for all the cases of signal sparsity and is applicable for signals that are sparse in any basis, hence universal.
Highlights
CS is the technique which allows sub-Nyquist sampling of sparse signals
The 3 cases of signal sparsity i.e. when signal is sparse in co-ordinate basis, orthonormal basis and redundant dictionary [9], is used to study the effect of mutual coherence on signal recovery and performance of different measurement matrices shown in Fig.1 is evaluated in terms of recovery error and recovery time
In this paper, performance of different measurement matrices is evaluated in terms of recovery error and recovery time
Summary
Article History:Received: november 2020; Accepted: 27 December 2020; Published online: 05 April 2021 ABSTRACT : Compressed Sensing (CS) avails mutual coherence metric to choose the measurement matrix that is incoherent with dictionary matrix. Random measurement matrices are incoherent with any dictionary, but their highly uncertain elements necessitate large storage and make hardware realization difficult. To avoid the randomness completely, deterministic sub-sampling is done by choosing rows deterministically rather than randomly, so that matrix can be regenerated during reconstruction without storing it. Matrices are generated by orthonormalization, which makes them highly incoherent with any dictionary basis. DFT matrix is found to be effective in terms of recovery error and recovery time for all the cases of signal sparsity and is applicable for signals that are sparse in any basis, universal.
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