Abstract
Co-sparse analysis model based-compressive sensing (CAMBCS) has gained attention in recent years as alternative to conventional sparse synthesis model based (SSMB)-CS. The equivalent operator as counterpart of the equivalent dictionary in the SSMB-CS is introduced in the CAMB-CS as the product of projection matrix and transpose of the analysis dictionary. This paper proposes an algorithm for designing suitable projection matrix for CAMB-CS by minimizing the mutual coherence of the equivalent operator based on equiangular tight frames design. The simulation results show that the CAMB-CS with the proposed projection matrix outperforms the SSMB-CS in terms of the signal quality reconstruction.
Highlights
Compressive sensing (CS) as a new paradigm in signal acquisition has gained popularity over the last decade after it was introduced in [1,2]
This paper addresses how to design a projection matrix for Co-sparse analysis model based (CAMB)-CS, use it to perform CS on a natural image and compare the image reconstruction performance to synthesis model based (SSMB)-CS
The OMP [23] and its counterpart Greedy algorithm GAP [6] were used for SSMB-CS and CAMB-CS respectively to obtain each reconstructed patch xj 64 1 and the whole reconstructed patches are arranged to get the reconstructed image I
Summary
Compressive sensing (CS) as a new paradigm in signal acquisition has gained popularity over the last decade after it was introduced in [1,2]. Co-sparse analysis model based (CAMB)-CS has attracted attention in recent years because it outperforms the synthesis model as shown in [7,8]. Three main problems of CS are how to build a dictionary, design a proper projection matrix and reconstruct the signal from CS. The famous KSVD algorithm and its extensions have been commonly used to build a synthesis dictionary [9,10] the improvements by exploiting additional structure of sparse coefficients can be found in [11,12]. While how to design optimal projection matrix for sparse synthesis model based (SSMB)-CS has been widely proposed such as in [18,19] but for CAMB-CS has not received attention. This paper addresses how to design a projection matrix for CAMB-CS, use it to perform CS on a natural image and compare the image reconstruction performance to SSMB-CS
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