Weighted ${\ell}_{{1}}$-minimization for sparse recovery under arbitrary prior information

Needell, Deanna; Saab, Rayan; Woolf, Tina

doi:10.1093/imaiai/iaw023

Cited by 22 publications

(20 citation statements)

References 44 publications

(102 reference statements)

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“…It is again confirmed that a multi-level weighting scheme can enhance the recovery performance. The tuning of the weights in [11] is achieved based on empirical results rather than theoretical findings.…”

Section: B Related Work and Key Differencesmentioning

confidence: 99%

Exploiting Prior Information in Block-Sparse Signals

Daei

Haddadi

Amini

2019

IEEE Trans. Signal Process.

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We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using an 1,2 optimization problem. In applications such as DNA micro-arrays, some extra information about the distribution of non-zero blocks is available; i.e., the number of non-zero blocks in certain subsets of the blocks is known. A typical way to consider the extra information in recovery procedures is to solve a weighted 1,2 problem. In this paper, we consider a block-sparse model which is accompanied with a partitioning of the blocks; besides the overall block-sparsity level of the signal, we assume to know the block-sparsity of each subset in the partition. Our goal in this work is to minimize the number of required linear measurements for perfect recovery of the signal by tuning the weights of a weighted 1,2 problem. For this goal, we apply tools from conic integral geometry and derive closedform expressions for the optimal weights. We show through precise analysis and simulations that the weighted 1,2 problem with optimal weights significantly outperforms the regular 1,2 problem. We further show that the optimal weights are robust against the inaccuracies of prior information.Index Terms-block-sparse, prior information, weighted 1,2, conic integral geometry.

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Section: B Related Work and Key Differencesmentioning

confidence: 99%

Exploiting Prior Information in Block-Sparse Signals

Daei

Haddadi

Amini

2019

IEEE Trans. Signal Process.

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“…There have also been some research efforts that aim at exploiting additional knowledge about the signal to further improve the sensing information recovery [23][24][25][26][27][28][29]. For instance, [23] proposes a ℓ 1 −minimization based approach that exploits knowledge about the support 1 of the sparse signal to recover information from noise-free measurements.…”

Section: A Related Workmentioning

confidence: 99%

“…They show that this recovery approach is more stable and robust than standard ℓ 1 −minimization approaches when 50% of the support is estimated correctly. This approach has been generalized for multiple weights in [25], addressing the case where the support is estimated with different confidence levels. These approaches, however, work well in applications where the support does not change much over time, like real-time dynamic MRI [23] and video/audio decoding [24,25] applications.…”

Section: A Related Workmentioning

confidence: 99%

“…This approach has been generalized for multiple weights in [25], addressing the case where the support is estimated with different confidence levels. These approaches, however, work well in applications where the support does not change much over time, like real-time dynamic MRI [23] and video/audio decoding [24,25] applications. In the wideband spectrum sensing case where the signal support changes over time, an estimate of the support is too difficult to acquire in advance, making these approaches unsuitable.…”

Section: A Related Workmentioning

confidence: 99%

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Efficient Spectrum Availability Information Recovery for Wideband DSA Networks: A Weighted Compressive Sampling Approach

Khalfi

Hamdaoui

Guizani

2018

IEEE Trans. Wireless Commun.

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Compressive sampling has great potential for making wideband spectrum sensing possible at sub-Nyquist sampling rates. As a result, there have recently been research efforts that leverage compressive sampling to enable efficient wideband spectrum sensing. These efforts consider homogenous wideband spectrum, where all bands are assumed to have similar PU traffic characteristics. In practice, however, wideband spectrum is not homogeneous, in that different spectrum bands could present different PU occupancy patterns. In fact, the nature of spectrum assignment, in which applications of similar types are often assigned bands within the same block, dictates that wideband spectrum is indeed heterogeneous. In this paper, we consider heterogeneous wideband spectrum, and exploit its inherent, blocklike structure to design efficient compressive spectrum sensing techniques that are well suited for heterogeneous wideband spectrum. We propose a weighted ℓ1−minimization sensing information recovery algorithm that achieves more stable recovery than that achieved by existing approaches while accounting for the variations of spectrum occupancy across both the time and frequency dimensions. In addition, we show that our proposed algorithm requires a lesser number of sensing measurements when compared to the state-of-the-art approaches.Index Terms-Wideband spectrum sensing; compressive sampling; heterogeneous wideband spectrum occupancy.

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“…To solve the analysis based problem (Equation )), the greedy‐type algorithms such as Greedy Analysis Pursuit 12‐14 or thresholding‐based methods such as iterative hard thresholding (IHT) have been proposed 15 . Several modifications of the greedy algorithms, incorporated partially known support information, have been performed for compressed sensing 16 . Modification of the IHT, 17 Binary Iterative Hard Thresholding (BIHT), 18 Orthogonal Matching Pursuit (OMP), 19 Compressive Sampling Matching Pursuit (CoSaMP), 20 and re‐weighted least squares 21 algorithms were studied in References 22‐24.…”

Section: Introductionmentioning

confidence: 99%

An enhanced weighted greedy analysis pursuit algorithm with application to EEG signal reconstruction

Mohagheghian

Deevband

Samadzadehaghdam

et al. 2020

Int J Imaging Syst Tech

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In the past decade, compressed sensing (CS) has provided an efficient framework for signal compression and recovery as the intermediate steps in signal processing. The well‐known greedy analysis algorithm, called Greedy Analysis Pursuit (GAP) has the capability of recovering the signals from a restricted number of measurements. In this article, we propose an extension to the GAP to solve the weighted optimization problem satisfying an inequality constraint based on the Lorentzian cost function to modify the EEG signal reconstruction in the presence of heavy‐tailed impulsive noise. Numerical results illustrate the effectiveness of our proposed algorithm, called enhanced weighted GAP (ewGAP) to reinforce the efficiency of the signal reconstruction and provide an appropriate candidate for compressed sensing of the EEG signals. The suggested algorithm achieves promising reconstruction performance and robustness that outperforms other analysis‐based approaches such as GAP, Analysis Subspace Pursuit (ASP), and Analysis Compressive Sampling Matching Pursuit (ACoSaMP).

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Weighted ${\ell}_{{1}}$-minimization for sparse recovery under arbitrary prior information

Cited by 22 publications

References 44 publications

Exploiting Prior Information in Block-Sparse Signals

Exploiting Prior Information in Block-Sparse Signals

Efficient Spectrum Availability Information Recovery for Wideband DSA Networks: A Weighted Compressive Sampling Approach

An enhanced weighted greedy analysis pursuit algorithm with application to EEG signal reconstruction

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