An approximate L0 norm minimization algorithm for compressed sensing

Hyder, Mashud; Mahata, Kaushik

doi:10.1109/icassp.2009.4960346

Cited by 37 publications

(15 citation statements)

References 9 publications

(13 reference statements)

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“…0 sparsity based approaches have been widely used in many vision and graphic tasks and acquired superior performance. Hyder and Mahata [23] proposed an iteratively approximate 0 -norm based on fixed point to reconstruct sparse signal and achieved an obvious improvement in noisy environment. In [10,24], Xu et al developed 0 gradient minimization to control the nonzero gradients among neighborhoods, which indicated that the prominent image structures needed to be preserved in image smoothing.…”

Section: Related Workmentioning

confidence: 99%

l0Sparsity for Image Denoising with Local and Global Priors

Gao

Wang

et al. 2015

Advances in Multimedia

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We propose al0sparsity based approach to remove additive white Gaussian noise from a given image. To achieve this goal, we combine the local prior and global prior together to recover the noise-free values of pixels. The local prior depends on the neighborhood relationships of a search window to help maintain edges and smoothness. The global prior is generated from a hierarchicall0sparse representation to help eliminate the redundant information and preserve the global consistency. In addition, to make the correlations between pixels more meaningful, we adopt Principle Component Analysis to measure the similarities, which can be both propitious to reduce the computational complexity and improve the accuracies. Experiments on the benchmark image set show that the proposed approach can achieve superior performance to the state-of-the-art approaches both in accuracy and perception in removing the zero-mean additive white Gaussian noise.

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Section: Related Workmentioning

confidence: 99%

l0Sparsity for Image Denoising with Local and Global Priors

Gao

Wang

et al. 2015

Advances in Multimedia

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“…However this algorithm is known to be NP-hard [12] for the same reason as RIP checking is NP-hard. This would seem to be a serious road-block.…”

Section: Recovery Algorithmsmentioning

confidence: 99%

Gravity Gradiometry: A Novel Application for Compressed Sensing

McNally¹

2013

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Abstract-During the past decade, compressed sensing (CS) has proven to be extremely useful for sparse signal reconstruction. Here the method of CS is applied to fast mass distribution determination based on cold atom gravity gradiometer measurements. Specifically we consider an array of M gradiometers placed around a 2D target area in order to determine the interior mass distribution in cases where the set of (M) sensor measurements under samples the distribution. This was done by assuming that the system's sparsity comes from the mass distributions only having K non-zero masses, which led to a non-orthogonal basis dictionary. This lack of orthogonality caused interesting behaviors, including weakened noise performance, and breaking of the typical CS motivated logarithmic scaling of required M values for larger K values. However, for low K values M scaled as expected. Modifications to the gravity sensor model to promote orthogonality and test its impact on signal recovery postponed the onset of anomalous scaling; suggesting that lack of orthogonality is the primary cause. While CS works for this sparse, but intrinsically ill-posed problem, this sensor system displayed increased noise sensitivity and a smaller upper bound on the size of recoverable K sets. However, while these limitations decrease CS performance, significant improvements over traditional sensing approaches are still possible.

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“…The ℓ 2 − ℓ 0 approach has been shown in the literature to be advantageous in many applications, for instance sparse component analysis [44], compressive sensing [32], matrix completion [41], robust regression [42], segmentation [52], and image recovery [20,49]. This paper mainly addresses the latter problem, where ℓ 2 − ℓ 0 is recognized for its ability to preserve edges between homogeneous regions [45].…”

Section: Introductionmentioning

confidence: 99%

A Majorize-Minimize Subspace Approach for $\ell_2-\ell_0$ Image Regularization

Chouzenoux¹,

Jezierska²,

Pesquet³

et al. 2013

SIAM J. Imaging Sci.

104

147

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In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes edge preserving measures or frame-analysis potentials commonly used in image processing. As shown by our asymptotic results, the ℓ 2 − ℓ 0 penalties we consider may be employed to provide approximate solutions to ℓ 0penalized optimization problems. One of the advantages of the proposed approach is that it allows us to derive an efficient Majorize-Minimize subspace algorithm. The convergence of the algorithm is investigated by using recent results in nonconvex optimization. The fast convergence properties of the proposed optimization method are illustrated through image processing examples. In particular, its effectiveness is demonstrated on several data recovery problems. * A preliminary version of this work has appeared in [18].

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An approximate L0 norm minimization algorithm for compressed sensing

Cited by 37 publications

References 9 publications

l0Sparsity for Image Denoising with Local and Global Priors

l0Sparsity for Image Denoising with Local and Global Priors

Gravity Gradiometry: A Novel Application for Compressed Sensing

A Majorize-Minimize Subspace Approach for $\ell_2-\ell_0$ Image Regularization

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