Compressed sensing, the ASBSR-method of image sampling and reconstruction and the problem of digital image acquisition with the 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. It is revealed that the compressed sensing approach, which was advanced as a solution to the sampling rate minimization problem, is far from reaching the sampling rate theoretical minimum. Potentials and limitations of compressed sensing are demystified using a simple and intutive model. 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 verification of the ASBSR-method and its possible applicability extensions to solving various underdetermined inverse problems such as color image demosaicing, image inpainting, 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.