A good and practical alternative to compressed sensing

What is it about?

Contemporary digital display devices and image processing software assume by default that sampling over regular square sampling grids is used. It is well known, that digital images acquired in this way are, as a rule, highly compressible. The phenomenon of ubiquitous compressibility of images raises very natural question: is it possible just directly measure the minimal amount of data that won’t end up being thrown away? These questions were apparently first posed by the inventors of the Compressed Sensing approach as a solution to this problem. However it turns out that compressed sensing methods are still far from reaching the theoretical minimum of signal sampling rate. In this paper we suggest an efficient practical image sampling method that enables reaching sampling rates sufficiently close to the minimum determined by the sampling theory. Compared to compressed sensing, the method provides the least redundant sampled representation of images, secures required image resolution and is robust to image sensor noise. It also shown that the proposed approach can be also used for solving other under-determined inverse problems in digital imaging

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