Topic
Compressed sensing
About: Compressed sensing is a research topic. Over the lifetime, 16412 publications have been published within this topic receiving 358493 citations. The topic is also known as: compressive sensing & compressive sampling.
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TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.
3,970 citations
TL;DR: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate, called compressive sensing, which employs nonadaptive linear projections that preserve the structure of the signal.
Abstract: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process.
3,555 citations
TL;DR: This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method.
Abstract: Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ) error term combined with a sparseness-inducing regularization term. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.
3,488 citations
TL;DR: Candes et al. as discussed by the authors established new results about the accuracy of the reconstruction from undersampled measurements, which improved on earlier estimates, and have the advantage of being more elegant. But they did not consider the restricted isometry property of the sensing matrix.
3,421 citations
TL;DR: This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task and was the first known method to offer near-optimal guarantees on resource usage.
Abstract: Compressive sampling (CoSa) is a new paradigm for developing data sampling technologies It is based on the principle that many types of vector-space data are compressible, which is a term of art in mathematical signal processing The key ideas are that randomized dimension reduction preserves the information in a compressible signal and that it is possible to develop hardware devices that implement this dimension reduction efficiently The main computational challenge in CoSa is to reconstruct a compressible signal from the reduced representation acquired by the sampling device This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task It was the first known method to offer near-optimal guarantees on resource usage
2,928 citations