Compressive Sensing - Mathematical Principles and Practical Implications-

Abstract

The mathematical foundations of the compressive sensing which goes against the common wisdom of data acquisition (the Nyquist-Shannon theorem) is reviewed. The compressive sensing asserts that one can reconstruct images or signals of interest accurately from a number of samples far smaller than the desired resolution of the image (e.g., the number of pixels in the image). The compressive sensing has far reaching implications. It suggests the new data acquisition protocols that translates analog information to digital form with fewer sensors considered necessary.

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