Compressed Sensing, ASBSR-method of image sampling and reconstruction and the problem of digital image acquisition with lowest possible sampling rate

The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling rate sufficient for signal reconstruction with a given accuracy is equal to the spectrum sparsity of the signal sparse approximation that has this accuracy. The capability of Compressed Sensing of reconstruction of signals sampled with aliasing is demystified using a simple and intutive model and limitations of this capability are discussed. It is revealed that the Compressed Sensing approach advanced as a solution to the sampling rate minimization problem is far from reaching the sampling rate theoretical minimum. A method of image Arbitrary Sampling and Bounded Spectrum Reconstruction (ASBSR-method) is described that allows to draw near the image sampling rate theoretical minimum. Presented and discussed are also results of experimental verifications 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 module of its Fourier spectrum and image reconstruction from its sparse samples in Fourier domain.