Cosparse analysis modeling - uniqueness and algorithms

Nam, Sangnam; Davies, Michael; Elad, Michael; Gribonval, Rémi

doi:10.1109/icassp.2011.5947680

Cited by 60 publications

(54 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Co-sparse method provides robust and unique approach of the linear problem in digital image processing model. Inspired from the basic concept of co-sparse analysis [27]. In sparse by using the operator function sometime image is not sparse, but its gradient can sparse [28].…”

Section: Co-sparse Signal Analysis Methodsmentioning

confidence: 99%

Image Super-Resolution Reconstruction Using Adaptive Co-sparse Regularization with Dual Dictionary

Sheikh¹,

Cao²,

Wang³

2016

IJMO

View full text Add to dashboard Cite

Abstract-This paper present a new method based on co-sparse with learning paired dictionary. The new framework is consisted of three parts. Firstly a paired dictionary have been learned which is used to overcome a low resolution image by utilizing an externally applied high resolution (HR) dictionary and then learn based on the internal dictionary. Process the paired dictionary which consists of low resolution (LR) and high resolution (HR) dictionary by kernel regression based on their coefficient respectively, and applied directly to construct the HR patches. Secondly, co-sparse regularization and features of self similarity have been introduced to strengthen and enhanced the image structure. In addition, propagation filtering is applied to suppress the artefacts generated from neighboring pixel of an image while reserving the image edges. Finally, the HR image is generated by reconstructing all superior HR patches. The effectiveness of the co-sparse demonstrated in real test images. The proposed method achieved good quality high resolution images that are superior compared with different SR methods in terms of peak signal to noise ratio (PSNR), and structural similarity (SSIM). IndexTerms-Dual dictionary, image resolution, propagation filter, self-similarity.

show abstract

Section: Co-sparse Signal Analysis Methodsmentioning

confidence: 99%

Image Super-Resolution Reconstruction Using Adaptive Co-sparse Regularization with Dual Dictionary

Sheikh¹,

Cao²,

Wang³

2016

IJMO

View full text Add to dashboard Cite

show abstract

“…Theoretical results concerning cosparsity may be found in [NDEG11,NDEG12]. We also consider the noisy case.…”

Section: Inpainting Via 1 Minimizationmentioning

confidence: 99%

Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis

2013

View full text Add to dashboard Cite

Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpainting. However, a mathematical analysis of these techniques which reveals the underlying geometrical content is completely missing. In this paper, we provide the first comprehensive analysis in the continuum domain utilizing the novel concept of clustered sparsity, which besides leading to asymptotic error bounds also makes the superior behavior of directional representation systems over wavelets precise. First, we propose an abstract model for problems of data recovery and derive error bounds for two different recovery schemes, namely 1 minimization and thresholding. Second, we set up a particular microlocal model for an image governed by edges inspired by seismic data as well as a particular mask to model the missing data, namely a linear singularity masked by a horizontal strip. Applying the abstract estimate in the case of wavelets and of shearlets we prove that -provided the size of the missing part is asymptotically to the size of the analyzing functions -asymptotically precise inpainting can be obtained for this model. Finally, we show that shearlets can fill strictly larger gaps than wavelets in this model.

show abstract

“…Traditionally, a representation model decomposes the signal into a linear combination of a few columns chosen from a predefined dictionary (representation matrix). Recently, a new signal model, called cosparse analysis model, was proposed [26].…”

Section: Multi-structural Signal Modelmentioning

confidence: 99%

Multi-structural Signal Recovery for Biomedical Compressive Sensing

Liu

Vos

Gligorijević

et al. 2013

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from subNyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have additional structures, such as multi-sparsity in different domains, piecewise smoothness, low rank, etc.We propose a framework to exploit all the available structure information. A new convex programming problem is JOURNAL NAME, VOL. X, NO. X, MONTH YEAR 2 generated with multiple convex structure-inducing constraints and the linear measurement fitting constraint. With additional a priori information for solving the underdetermined system, the signal recovery performance can be improved. In numerical experiments, we compare the proposed method with classical methods. Both simulated data and real-life biomedical data are used. Results show that the newly proposed method achieves better reconstruction accuracy performance in term of both L1 and L2 errors.

show abstract

Cosparse analysis modeling - uniqueness and algorithms

Cited by 60 publications

References 10 publications

Image Super-Resolution Reconstruction Using Adaptive Co-sparse Regularization with Dual Dictionary

Image Super-Resolution Reconstruction Using Adaptive Co-sparse Regularization with Dual Dictionary

Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis

Multi-structural Signal Recovery for Biomedical Compressive Sensing

Contact Info

Product

Resources

About