Strong thresholds for &amp;#x2113;&lt;inf&gt;2&lt;/inf&gt;/&amp;#x2113;&lt;inf&gt;1&lt;/inf&gt;-optimization in block-sparse compressed sensing

Stojnic, Mihailo

doi:10.1109/icassp.2009.4960261

Cited by 14 publications

(38 citation statements)

References 29 publications

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“…3.13] Our applications focus on these four instances, but a dizzying variety other structure-promoting atomic gauges are available. For example, there are atomic gauges for vectors that are sparse in a dictionary (also known as analysis-sparsity) [34], [11], block-and group-sparse vectors [20], [72], and low-rank tensors and probability measures [15, Sec. 2].…”

Section: Structured Signals and Atomic Gaugesmentioning

confidence: 99%

Sharp Recovery Bounds for Convex Demixing, with Applications

2014

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Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these demixing problems, and many others. This work introduces a randomized signal model which ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, this approach identifies a summary statistic that reflects the complexity of a particular signal. The difficulty of separating two structured, incoherent signals depends only on the total complexity of the two structures. Some applications include (i) demixing two signals that are sparse in mutually incoherent bases; (ii) decoding spread-spectrum transmissions in the presence of impulsive errors; and (iii) removing sparse corruptions from a low-rank matrix. In each case, the theoretical analysis of the convex demixing method closely matches its empirical behavior.Communicated by Emmanuel Candès.

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Section: Structured Signals and Atomic Gaugesmentioning

confidence: 99%

Sharp Recovery Bounds for Convex Demixing, with Applications

2014

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“…Dynamic extensions of these ideas should prove to be useful in applications where the structure is present and changes slowly. Two common examples of structured sparsity are block sparsity [114], [115] and tree structured sparsity (for wavelet coefficients) [116]. A length m vector is block sparse if it can be partitioned into length k blocks such that a lot of the blocks are entirely zero.…”

Section: A Signal Models 1) Structured Sparsitymentioning

confidence: 99%

“…A length m vector is block sparse if it can be partitioned into length k blocks such that a lot of the blocks are entirely zero. One way to recover block sparse signals is by solving the ℓ 2ℓ 1 minimization problem [114], [115]. Block sparsity is valid for many applications, e.g., for the foreground image sequence of a video consisting of one or a few moving objects, or for the activation regions in brain fMRI.…”

Section: A Signal Models 1) Structured Sparsitymentioning

confidence: 99%

Recursive Recovery of Sparse Signal Sequences From Compressive Measurements: A Review

Vaswani

Zhan

2016

IEEE Trans. Signal Process.

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Abstract-In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change with time, although, in many practical applications, the changes are gradual. An important class of applications where this problem occurs is dynamic projection imaging, e.g., dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology, or dynamic computed tomography.

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“…To exploit the block structure of ideally block-sparse signals, C 2 /C 1 optimization was proposed. The standard block sparse constraint (SBSC) in the form of C 2 /C 1 optimization can be formulated as [35] [36]:…”

Section: A Wideband Spectrum Sensing For Fixed Spectrum Allocationmentioning

confidence: 99%

Enhanced compressive wideband frequency spectrum sensing for dynamic spectrum access

Liu

Wan

2012

EURASIP J. Adv. Signal Process.

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Wideband spectrum sensing detects the unused spectrum holes for dynamic spectrum access (DSA). Too high sampling rate is the main challenge. Compressive sensing (CS) can reconstruct sparse signal with much fewer randomized samples than Nyquist sampling with high probability. Since survey shows that the monitored signal is sparse in frequency domain, CS can deal with the sampling burden. Random samples can be obtained by the analog-to-information converter. Signal recovery can be formulated as the combination of an L0 norm minimization and a linear measurement fitting constraint. In DSA, the static spectrum allocation of primary radios means the bounds between different types of primary radios are known in advance. To incorporate this a priori information, we divide the whole spectrum into sections according to the spectrum allocation policy. In the new optimization model, the minimization of the L2 norm of each section is used to encourage the cluster distribution locally, while the L0 norm of the L2 norms is minimized to give sparse distribution globally. Because the L2/L0 optimization is not convex, an iteratively re-weighted L2/L1 optimization is proposed to approximate it. Simulations demonstrate the proposed method outperforms others in accuracy, denoising ability, etc.

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Strong thresholds for ℓ<inf>2</inf>/ℓ<inf>1</inf>-optimization in block-sparse compressed sensing

Cited by 14 publications

References 29 publications

Sharp Recovery Bounds for Convex Demixing, with Applications

Sharp Recovery Bounds for Convex Demixing, with Applications

Recursive Recovery of Sparse Signal Sequences From Compressive Measurements: A Review

Enhanced compressive wideband frequency spectrum sensing for dynamic spectrum access

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