Stochastic CoSaMP: Randomizing Greedy Pursuit for Sparse Signal Recovery

Pal, Dipan K.; Mengshoel, Ole J.

doi:10.1007/978-3-319-46128-1_48

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…23 Our approach will be in the spirit of random subdictionary selection. 24 There have been some approaches with subsampling of dictionaries over rows and columns in order to increase the speed of the convergence of greedy methods, 25,26 but using such subsampling methods for coherent dictionaries is still unexplored. Authors of these papers named one of these methods as StoCoSaMP (Stochastic CoSaMP).…”

Section: The Recovery Of Signal's Support In a Highly Coherent Dictiomentioning

confidence: 99%

Localization of sound sources in a room with one microphone

Tukuljac

Lissek

2017

Wavelets and Sparsity XVII

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Estimation of the location of sound sources is usually done using microphone arrays. Such settings provide an environment where we know the difference between the received signals among different microphones in the terms of phase or attenuation, which enables localization of the sound sources. In our solution we exploit the properties of the room transfer function in order to localize a sound source inside a room with only one microphone. The shape of the room and the position of the microphone are assumed to be known. The design guidelines and limitations of the sensing matrix are given. Implementation is based on the sparsity in the terms of voxels in a room that are occupied by a source. What is especially interesting about our solution is that we provide localization of the sound sources not only in the horizontal plane, but in the terms of the 3D coordinates inside the room.

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Section: The Recovery Of Signal's Support In a Highly Coherent Dictiomentioning

confidence: 99%

Localization of sound sources in a room with one microphone

Tukuljac

Lissek

2017

Wavelets and Sparsity XVII

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“…where c 0 = {the number of indices k such that c k = 0} measures the sparsity of c. In (6), δ is a tolerance of solution inaccuracy due to the truncation of the expansion. While, the problem (6) is NP-hard to solve, approximate solutions may be obtained in polynomial time using a variety of greedy algorithms including orthogonal matching pursuit (OMP) [29,30,31,32], compressive sampling matching pursuit (CoSaMP) [33,34], and subspace pursuit (SP) [35], or convex relaxation via ℓ 1 -minimization [5,6]. The key advantage of an approximation via compressed sensing is that, if the QoI is approximately sparse, stable and convergent approximations of c can be obtained using N < P random samples of u(Ξ), as long as Φ satisfies certain conditions [5,6,10,36,21,27].…”

Section: Introductionmentioning

confidence: 99%

Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Diaz

Doostan

Hampton

2018

Computer Methods in Applied Mechanics and Engineering

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In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this sparsity in order to reduce computational costs. A class of greedy compressed sensing algorithms use least squares minimization to approximate PC coefficients. This least squares problem lends itself to the theory of optimal design of experiments (ODE). Our work focuses on selecting an experimental design that improves the accuracy of sparse PC approximations for a fixed computational budget. We propose DSP, a novel sequential design, greedy algorithm for sparse PC approximation. The algorithm sequentially augments an experimental design according to a set of the basis polynomials deemed important by the magnitude of their coefficients, at each iteration. Our algorithm incorporates topics from ODE to estimate the PC coefficients. A variety of numerical simulations are performed on three physical models and manufactured sparse PC expansions to provide a comparative study between our proposed algorithm and other non-adaptive methods. Further, we examine the importance of sampling by comparing different strategies in terms of their ability to generate a candidate pool from which an optimal experimental design is chosen. It is demonstrated that the most accurate PC coefficient approximations, with the least variability, are produced with our design-adaptive greedy algorithm and the use of a studied importance sampling strategy. We provide theoretical and numerical results which show that using an optimal sampling strategy for the candidate pool is key, both in terms of accuracy in the approximation, but also in terms of constructing an optimal design.

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“…c where kck 0 = {the number of indices k such that c k = 6 0} indicates the sparsity c. In (12), δ is a tolerance of solution inaccuracy due to the truncation of the expansion. While, the problem (12) is NP-hard to solve, approximate solutions may be obtained in polynomial time using a variety of greedy algorithms including orthogonal matching pursuit (OMP) (Tropp and Gilbert 2005;Tropp and Gilbert 2007;Needell and Vershynin 2010;Davenport and Wakin 2010), compressive sampling matching pursuit (CoSaMP) (Needell and Tropp 2009;Pal and Mengshoel 2016), and subspace pursuit (SP) (Dai and Milenkovic 2009). A convex relaxation of (12) can also be solved via ` 1 -minimization (Candès and Wakin 2008;Donoho 2006).…”

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confidence: 99%