article · 2016
Compressed sensing
David Donoho, Yaakov Tsaig, David L. Donoho
Cited by 0Abstract and details only
Abstract
We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal number of pixels, and yet be accurately reconstructed. The samples are nonadaptive and measure ‘random ’ linear combinations of the transform coefficients. Approximate reconstruction is obtained by solving for the transform coefficients consistent with measured data and having the smallest possible `1 norm. We perform a series of numerical experiments which validate in general terms the basic idea proposed in [14, 3, 5], in the favorable case where the transform coefficients are sparse in the strong sense that the vast majority are zero. We then consider a range of less-favorable cases, in which the object has all coefficients nonzero, but the coefficients obey an `p bound, for some p ∈ (0, 1]. These experiments show that the basic inequalities behind the CS method seem to involve reasonable constants. We next consider synthetic examples modelling problems in spectroscopy and image pro-
Cite this paper
Donoho, D., Tsaig, Y., & Donoho, D. L. (2016). Compressed sensing.
Donoho, David, et al. “Compressed sensing.” 2016.
Donoho, David, Yaakov Tsaig, and David L. Donoho. 2016. “Compressed sensing.”
Donoho, D., Tsaig, Y. and Donoho, D.L. (2016) ‘Compressed sensing’.
@article{donoho2016compressed,
title = {{Compressed sensing}},
author = {Donoho, David and Tsaig, Yaakov and Donoho, David L.},
year = {2016}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.