arXiv subjects

L. Yaroslavsky

Publications and source records attributed to L. Yaroslavsky.

5 recordsLinked to original sources

arXiv2021

The General sampling theorem, Compressed sensing and a method of image sampling and reconstruction with sampling rates close to the theoretical limit

The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed sensing methods and a practical method of image sampling and reconstruction with sampling rates close to the theoretical minimum.

eess.IV↗

arXiv2015

Can compressed sensing beat the Nyquist sampling rate?

Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that, in a realistic scenario for signals that are believed to be sparse, one can achieve a substantially larger saving than compressing sensing can. It is also shown that frequent assertions in the literature that "Compressed sensing" can beat the Nyquist sampling approach are misleading substitution of terms and are rooted in misinterpretation of the sampling theory.

cs.IT↗

arXiv2015

Is "Compressed Sensing" compressive? Can it beat the Nyquist Sampling Approach?

Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary sampling with subsequent data compression is prohibitive, there is at least one more efficient, in terms of data compression capability, and more simple and intuitive alternative to Compressed sensing: random sparse sampling and restoration of image band-limited approximations based on energy compaction capability of transforms. It is also shown that assertions that "Compressed sensing" can beat the Nyquist sampling approach are rooted in misinterpretation of the sampling theory.

physics.optics↗

arXiv2009

Discrete Sampling Theorem, Sinc-lets and Other Peculiar Properties of Sampled Signals

Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from their sparse samples are discussed for different transforms and applications are illustrated by examples of image super-resolution from multiple chaotically sampled frames and in image reconstruction from projections. Experimental evidence is presented of the existence of discrete signals sharply bounded both in space and DFT or DCT domains and of the family of the corresponding basis functions

physics.optics↗

arXiv2007

Super-resolution in turbulent videos: making profit from damage

It is shown that one can make use of local instabilities in turbulent video frames to enhance image resolution beyond the limit defined by the image sampling rate. The paper outlines the processing algorithm, presents its experimental verification on simulated and real-life videos and discusses its potentials and limitations.

physics.optics↗