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<p>In this paper, we have addressed the issue of the sparse compression complexity for the speech signals. First of all, this work illustrated the effect of the signal length on the complexity levels of Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) algorithms. Also, this paper introduced a study of possibility to reduce that complexity by exploiting the shared atoms among the contiguous speech compressions. By comparing the shared atoms levels and a threshold level induced by an analytic model based on the both the central and non-central hyper-geometric distributions, we proved the ability of the shared atoms criterion to detect if there is biasing towards a subspace of atoms or not, and to decide if the biasing occurs due to the redundancy in the dictionary of atoms, or due to the redundancy in the signal itself. <br />Moreover, we suggested a subspace bias-based approaches for complexity reduction called "Atoms Reuse" and "Active Cluster". Both methods exploits the higher levels of the shared atoms to reduce the compression complexity by reducing the search space during the pursuit iterations.</p>

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This work comprises the development of a quality enhancement technique for image encoders that use compressive sensing. The recommended solution seeks to maximize the perceptual quality based objective function, unlike other sparse representation algorithms that minimizes the error-based objective function. The key idea behind this work is to develop an iterative methodology that works as a modifier for the sparse coefficients. The modification procedure is SSIM-based and has been carried out in an iterative and linear manner. The conducted experiments revealed that the recommended technique works better than another SSIM-based modifier termed the SSIM-inspired OMP (iOMP) in terms of SSIM levels gained. The t-test is also utilized to examine our performance for significance, and the results show that the method works well for any type of image and any size, especially when a data-independent based dictionary is used.INDEX TERMS Orthogonal matching pursuit, compressive sensing, structural similarity index, image enhancement.

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