Can compressed sensing beat the Nyquist sampling rate?

The 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. It is demonstrated on a simple and intuitive example, 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 substitutions of terms and are rooted in misinterpretation of the sampling theory.

[1]  Minh N. Do,et al.  A Theory for Sampling Signals from a Union of Subspaces , 2022 .

[2]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[3]  Barak Fishbain,et al.  Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[5]  Enrico Magli,et al.  Distributed Compressed Sensing , 2015 .

[6]  R. M. Willett,et al.  Compressed sensing for practical optical imaging systems: A tutorial , 2011, IEEE Photonics Conference 2012.

[7]  David L. Donoho,et al.  Precise Undersampling Theorems , 2010, Proceedings of the IEEE.

[8]  David L. Donoho,et al.  Exponential Bounds Implying Construction of Compressed Sensing Matrices, Error-Correcting Codes, and Neighborly Polytopes by Random Sampling , 2010, IEEE Transactions on Information Theory.

[9]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[10]  Adrian Stern,et al.  Compressed Imaging With a Separable Sensing Operator , 2009, IEEE Signal Processing Letters.

[11]  J M Nichols,et al.  Beating Nyquist with light: a compressively sampled photonic link. , 2011, Optics express.

[12]  Jonathan M. Nichols,et al.  Compressive Sensing Demystified , 2014 .