Publication

Optimal Sampling Rates in Infinite-Dimensional Compressed Sensing

Martin Vetterli, Loïc Arnaud Baboulaz, Mitra Fatemi
2013
Conference Papers

Abstract

The theory of compressed sensing studies the problem of recovering a high dimensional sparse vector from its projections onto lower dimensional subspaces. The recently introduced framework of infinite-dimensional compressed sensing [1], to some extent generalizes these results to infinite-dimensional scenarios. In particular, it is shown that the continuous-time signals that have sparse representations in a known domain can be recovered from random samples in a different domain. The range M and the minimum number m of samples for perfect recovery are limited by a balancing property of the two bases. In this paper, by considering Fourier and Haar wavelet bases, we experimentally show that M can be optimally tuned to minimize the number of samples m that guarantee perfect recovery. This study does not have any parallel in the finite-dimensional CS.

Official source

https://infoscience.epfl.ch/entities/publication/ea044d9d-abab-4d39-ac93-9101194da167

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Martin Vetterli, Loïc Arnaud Baboulaz, Mitra Fatemi
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ea044d9d-abab-4d39-ac93-9101194da167

About this result

Related concepts (32)

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Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.

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