Compressed Sensing: Methods, Theory and Applications presents and describes a method of image Arbitrary Sampling and Bounded Spectrum Reconstruction (ASBSR-method) that allows for drawing near the image sampling rate theoretical minimum. This compilationalso discusses results of experimental verification of the ASBSR-method and its possible applicability extensions to solving various underdetermined inverse problems such as: color image demosaicing, image in-painting, image reconstruction from their sparsely sampled or decimated projections, image reconstruction from the modulus of its Fourier spectrum, and image reconstruction from its sparse samples in Fourier domain. Following this, the authors examine a novel framework to obtain HR images from CS imaging systems capturing multiple Low Resolution (LR) images of the same scene. The assumption that when an image admits a sparse representation in a transformed domain, a blurred version of it will also be sparse in the transformed domain, allows for the recovery of blurred images from CS observations. This proposed Compressed Sensing Super Resolution (CSSR) approach, combines existing CS reconstruction algorithms with an LR to HR approach based on the use of a new robust sparsity promoting prior based onsuper Gaussian regularisation. Additionally, several image CS recovery methods are studied. The concept of CS in image processing is introduced and a brief description of an effective CS reconstruction algorithm, called block-based CS with smoothed-projected Landweber reconstruction (BCS-SPL), is presented. Next, an adaptive CS method is presented, which provides a higher recovered image quality with respect to the BCS-SPL algorithm--
