Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

Figueiredo, Mário A. T.; Nowak, Rob; Wright, Stephen J.

doi:10.1109/jstsp.2007.910281

Cited by 3,026 publications

(1,928 citation statements)

References 51 publications

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“…Of course, the original multi-view frames can be achieved by image reconstruction algorithms. A number of methods including minimum total variance (min-TV) [7], gradient projection sparse reconstruction (GPSR) [8], iterative greedy algorithm [9] and iterative threshold projection (ITP) [3] have been discussed in the literatures for the CS reconstruction. In this paper, the ITP algorithm is used to reconstruct the multi-view videos.…”

Section: Experiments Resultsmentioning

confidence: 99%

Adaptive Ratio for the Compressed Sensing of Multi-view Videos

Yang¹,

Chong²,

Li³

2018

dtcse

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Abstract. Most of the compressed sensing for multi-view videos always works on non-adaptive linear projections, and the ratio of compressive sampling is usually determined empirically. Consequently, the quality of reconstruction frames is always affected and limited. The paper is therefore proposed a method on the derivation of adaptive ratio for the compressive sensing of video frame. First of all, the block-based compressed sensing (BCS) with conventional selection for compressive measurements was reviewed. Then an estimation method for the sparsity of multi-view video frames was proposed with the two dimensional sparse transform (2DST). With an energy threshold determined beforehand, the DST coefficients were normalized and sorted by the descending order, and the sparsity of the multi-view video can be achieved by calculating the proportion of dominant coefficients. And finally, the simulation result shows that, the method can estimate the sparsity of a video frame effectively, and provides a basis for the selection of compressive measurement. The result also shows that the method can ensure the reconstruction quality of multi-view videos.

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Section: Experiments Resultsmentioning

confidence: 99%

Adaptive Ratio for the Compressed Sensing of Multi-view Videos

Yang¹,

Chong²,

Li³

2018

dtcse

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“…This algorithm is simple to implement, has low memory requirements and seems to be competitive with the more elaborated Cosso-based algorithm that is usually used in the statistical literature (see [19]). …”

Section: Grouped Lasso Regularizationmentioning

confidence: 99%

Penalized estimation in additive varying coefficient models using grouped regularization

Antoniadis¹,

Gijbels²,

Lambert-Lacroix³

2013

Stat Papers

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Additive varying coefficient models are a natural extension of multiple linear regression models, allowing the regression coefficients to be functions of other variables. Therefore these models are more flexible to model more complex dependencies in data structures. In this paper we consider the problem of selecting in an automatic way the significant variables among a large set of variables, when the interest is on a given response variable. In recent years several grouped regularization methods have been proposed and in this paper we present these under one unified framework in this varying coefficient model context. For each of the discussed grouped regularization methods we investigate the optimization problem to be solved, possible algorithms for doing so, and the variable and estimation consistency of the methods. We investigate the finite-sample performance of these methods, in a comparative study, and illustrate them on real data examples.

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“…This method was sped up by using separable sensing matrices as proposed in [2]. Also, we used for comparison one of the most efficient algorithms in the literature, -GPSR (Gradient Projection for Sparse Reconstruction) [10]. We did not compare the original TV-SBI algorithm [8] without separable sensing matrices because the computer runs out of memory even for moderate image sizes.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Total Variation Minimization with Separable Sensing Operator

Shishkin¹,

Wang²,

Hagen³

2010

Lecture Notes in Computer Science

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Abstract. Compressed Imaging is the theory that studies the problem of image recovery from an under-determined system of linear measurements. One of the most popular methods in this field is Total Variation (TV) Minimization, known for accuracy and computational efficiency. This paper applies a recently developed Separable Sensing Operator approach to TV Minimization, using the Split Bregman framework as the optimization approach. The internal cycle of the algorithm is performed by efficiently solving coupled Sylvester equations rather than by an iterative optimization procedure as it is done conventionally. Such an approach requires less computer memory and computational time than any other algorithm published to date. Numerical simulations show the improved -by an order of magnitude or more -time vs. image quality compared to two conventional algorithms.

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Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

Cited by 3,026 publications

References 51 publications

Adaptive Ratio for the Compressed Sensing of Multi-view Videos

Adaptive Ratio for the Compressed Sensing of Multi-view Videos

Penalized estimation in additive varying coefficient models using grouped regularization

Total Variation Minimization with Separable Sensing Operator

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