Recipes on hard thresholding methods

Kyrillidis, Anastasios; Cevher, Volkan

doi:10.1109/camsap.2011.6136024

Cited by 45 publications

(70 citation statements)

References 11 publications

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“…to obtain the final result (16). It is easy to check that the first iteration of the algorithm satisfies the recursion (15), completing the proof.…”

Section: Appendix a Proofs Of Key Resultsmentioning

confidence: 79%

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On accelerated hard thresholding methods for sparse approximation

Cevher¹

2011

SPIE Proceedings

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We propose and analyze acceleration schemes for hard thresholding methods with applications to sparse approximation in linear inverse systems. Our acceleration schemes fuse combinatorial, sparse projection algorithms with convex optimization algebra to provide computationally efficient and robust sparse recovery methods. We compare and contrast the (dis)advantages of the proposed schemes with the state-of-the-art, not only within hard thresholding methods, but also within convex sparse recovery algorithms.

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“…to obtain the final result (16). It is easy to check that the first iteration of the algorithm satisfies the recursion (15), completing the proof.…”

Section: Appendix a Proofs Of Key Resultsmentioning

confidence: 79%

“…To establish (16), we look at the single root of the characteristic equation of the series inequality defined by (15), which is given by ρ > 0, as defined in Proposition 1. Assuming ρ < 1, which defines the isometry requirements of the algorithm, the series is convergent.…”

Section: Appendix a Proofs Of Key Resultsmentioning

confidence: 99%

On accelerated hard thresholding methods for sparse approximation

Cevher¹

2011

SPIE Proceedings

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“…In this paper, we consider the algorithms based on iterative hard thresholding (IHT) (Blumensath and Davies, 2009;Kyrillidis and Cevher, 2011) as well the agglomorative greedy approach of orthogonal matching pursuit (OMP) to evaluate the combinatorial method to speech localization and separation incorporating the sparsity structures underlying spectrographic coefficients (Gribonval and Bacry, 2003).…”

Section: Methodsmentioning

confidence: 99%

“…We use the algorithm proposed in (Kyrillidis and Cevher, 2011) which is an accelerated scheme for hard thresholding methods with the following recursion…”

Section: Ihtmentioning

confidence: 99%

Computational methods for underdetermined convolutive speech localization and separation via model-based sparse component analysis

Asaei

Bourlard

Taghizadeh

et al. 2016

Speech Communication

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In this paper, the problem of speech source localization and separation from recordings of convolutive underdetermined mixtures is studied. The problem is cast as recovering the spatio-spectral speech information embedded in a microphone array compressed measurements of the acoustic field. A model-based sparse component analysis framework is formulated for sparse reconstruction of the speech spectra in a reverberant acoustic resulting in joint localization and separation of the individual sources. We compare and contrast the computational approaches to model-based sparse recovery exploiting spatial sparsity as well as spectral structures underlying spectrographic representation of speech signals. In this context, we explore identification of the sparsity structures at the auditory and acoustic representation spaces. The auditory structures are formulated upon the principles of structural grouping based on proximity, autoregressive correlation and harmonicity of the spectral coefficients and they are incorporated for sparse reconstruction. The acoustic structures are formulated upon the image model of multipath propagation and they are exploited to characterize the compressive measurement matrix associated with microphone array recordings.Three approaches to sparse recovery relying on combinatorial optimization, convex relaxation and Bayesian methods are studied and evaluated based on thorough experiments. The sparse Bayesian learning method is shown to yield better perceptual quality while the interference suppression is also achieved using the combinatorial approach with the advantage of offering the most efficient computational cost. Furthermore, it is demonstrated that an average autoregressive model can be learned for speech localization and exploiting the proximity structure in the form of block sparse coefficients enables accurate localization. Throughout the extensive empirical evaluation, we confirm that a large and random placement of the microphones enables significant improvement in source localization and separation performance.

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“…It also allows for greater adaptability to signal models using model-based CS [19]. The IHT can be further accelerated using techniques explored in detail in [20], [21], e.g., by adapting the step-size selection in each iteration.…”

Section: B Sparse Image Recoverymentioning

confidence: 99%

Sparse MIMO architectures for through-the-wall imaging

Boufounos

Liu

et al. 2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Compressive sensing and sparse array processing has provided new approaches to improve radar imaging systems. This paper, explores the potential of sparse Multiple-Input-Multiple-Output (MIMO) radar arrays to significantly reduce the cost of through-the-wall imaging (TWI). We analyze three well-known sparse array structures-nested arrays, co-prime arrays and random arrays-and examine their performance in the presence of common types of layered walls. The reconstruction is performed by formulating and solving a wall parameter estimation problem in conjunction with a sparse reconstruction problem that takes the wall parameters into account. Our simulation results demonstrate the effectiveness of our approach and validate the performance of the system for the three different MIMO sparse array structures. IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-Compressive sensing and sparse array processing has provided new approaches to improve radar imaging systems. This paper, explores the potential of sparse Multiple-Input-Multiple-Output (MIMO) radar arrays to significantly reduce the cost of through-the-wall imaging (TWI). We analyze three well-known sparse array structures-nested arrays, co-prime arrays and random arrays-and examine their performance in the presence of common types of layered walls. The reconstruction is performed by formulating and solving a wall parameter estimation problem in conjunction with a sparse reconstruction problem that takes the wall parameters into account. Our simulation results demonstrate the effectiveness of our approach and validate the performance of the system for the three different MIMO sparse array structures.Index Terms-Through-the-wall, MIMO sparse arrays, Sparse image reconstruction, compressive sensing.

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Recipes on hard thresholding methods

Cited by 45 publications

References 11 publications

On accelerated hard thresholding methods for sparse approximation

On accelerated hard thresholding methods for sparse approximation

Computational methods for underdetermined convolutive speech localization and separation via model-based sparse component analysis

Sparse MIMO architectures for through-the-wall imaging

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