Experimental Investigation for Practical Sparsity Number for Image Reconstruction Based on SL0 Algorithm in Discrete Frequency Domain

Compressive Sensing (CS) is known as a new sampling theory that use small number of basis elements for constructing of signals (or images) and these basis elements (so called sparsity number) are very important parameters that approximate how sparsify the image is. Due to several characteristics of each image groups, the sparsity number could be varied and there is unfortunately very little research for this issue. This paper presents two main contributions: First, this paper proposes a practical sparsity number estimation technique using for an image reconstruction for SL0 algorithm based on Discrete Cosine Transform domain (DCT). Second the practical sparsity number of difference image groups is the experiment based on over 2000 images. The DCT is exclusively applied for a sparse representation of images because it is proven as a useful instrument for image analysis and processing. In general, images can be represented by a linear superposition of small number of wavelet elements selected from a suitable filter. The proposed models process the image with Smoothed norm algorithm. This algorithm stated that if signal or image is sufficiently sparse, we can reconstruct it from small amount of none zero basis components. The experiment is comprehensively tested under 2000 sampling images that are categorized in 18 groups by their characteristics. Moreover this sparsity number is practically used for any CS algorithm based on DCT domain.