Cosparse analysis model-based compressive sensing with optimized projection matrix

The Compressive Sensing (CS) technique provides a signal acquisition dimensional reduction by multiplying a projection matrix with the signal. Until now, the projection matrix optimization is commonly performed using the Sparse Synthesis Model-Based (SSMB), where it takes a linear combination of a few atoms in a synthesis dictionary to form a signal. The Cosparse Analysis Model-Based (CAMB) provides an alternative model where the multiplication of the signal with an analysis dictionary (operator) produces a cosparse coefficient. The CAMB-CS method is proposed in this paper by taking into account the amplified Cosparse Representation Error (CSRE) parameter and the relative amplified CSRE optimize the projection matrix, in addition to the mutual coherence parameter. The optimized projection matrix in CAMB-CS is obtained using an alternating minimization algorithm and nonlinear conjugation gradient method. In the optimization algorithm, the Gaussian random matrix is used as the initial projection matrix. The simulation results showed an increase in the Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) of the reconstructed image in the CAMB-CS system up to 10.23% and 8.46%, respectively, compared to the Gaussian random matrix. Compared to the SSMB-CS optimized projection matrix, the developed method increases the PSNR and SSIM of the recovered image up to 21.21% and 17.11%, respectively.