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The problem of minimization of the number of measurements needed for digitalimage acquisition and reconstruction with a given accuracy is addressed. Basicsof the sampling theory are outlined to show that the lower bound of signalsampling rate sufficient for signal reconstruction with a given accuracy isequal to the spectrum sparsity of the signal sparse approximation that has thisaccuracy. It is revealed that the compressed sensing approach, which wasadvanced as a solution to the sampling rate minimization problem, is far fromreaching the sampling rate theoretical minimum. Potentials and limitations ofcompressed sensing are demystified using a simple and intutive model, A methodof image Arbitrary Sampling and Bounded Spectrum Reconstruction (ASBSR-method)is described that allows to draw near the image sampling rate theoreticalminimum. Presented and discussed are also results of experimental verificationof the ASBSR-method and its possible applicability extensions to solvingvarious underdetermined inverse problems such as color image demosaicing, imagein-painting, image reconstruction from their sparsely sampled or decimatedprojections, image reconstruction from the modulus of its Fourier spectrum, andimage reconstruction from its sparse samples in Fourier domain

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