An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

Daubechies, Ingrid; Defrise, Michel; Mol, Christine De

doi:10.1002/cpa.20042

Cited by 4,162 publications

(3,681 citation statements)

References 45 publications

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“…The sparsity of nature images under these tight frames has been successfully used to solve many image restoration tasks including image denoising, non-blind image deblurring, image inpainting, etc (e.g. [12,6,4]). Therefore, we believe that the high sparsity of images under certain suitable tight frame system is also a good regularization on the latent image in our blind deblurring problem.…”

Section: Our Approachmentioning

confidence: 99%

Blind motion deblurring from a single image using sparse approximation

Cai¹,

Jiang²,

Liu³

et al. 2009

2009 IEEE Conference on Computer Vision and Pattern Recognition

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Restoring a clear image from a single motion-blurred image due to camera shake has long been one challenging problem in digital imaging. Existing blind deblurring techniques either only can remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images.

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Section: Our Approachmentioning

confidence: 99%

Blind motion deblurring from a single image using sparse approximation

Cai¹,

Jiang²,

Liu³

et al. 2009

2009 IEEE Conference on Computer Vision and Pattern Recognition

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“…Two major categories of such techniques include parallel imaging (PI) [3]- [5] and compressed sensing (CS) [6]. While with PI missing k-space data are interpolated based on a priori knowledge of the coil sensitivity profiles, CS interpolates the missing data by imposing an a priori transform domain sparsity constraint to regularize the reconstruction problem [7]. Due to the independence of CS and PI reconstruction constraints, a combined CS and PI reconstruction allows for further acceleration [8].…”

Section: Introductionmentioning

confidence: 99%

Diagnostic quality assessment of compressed sensing accelerated magnetic resonance neuroimaging

Kayvanrad

Lin

Joshi

et al. 2016

Magnetic Resonance Imaging

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Purpose: The aim of this study was to determine the efficacy of compressed sensing reconstructions for specific clinical neuroimaging applications of magnetic resonance imaging beyond more conventional k-space under-sampling approaches such as parallel imaging and simple low-resolution acquisitions.Methods: Four routine clinical neuroimaging pulse sequences were chosen for this study due to their long acquisition time. In a series of blinded studies, three board-certified radiologists independently evaluated compressed sensing, parallel imaging, and low-resolution images at up to 5x accelerations. Experiments on synthetic brain images with artificial but realistic lesions were carried out to assess diagnostic accuracy for the detection of non-specific white matter lesions, permitting controlled evaluation of shift-variant compressed sensing reconstructions.Results: Ringing and blurring were identified as the primary artifacts that hinder diagnostic quality of combined compressed sensing and parallel imaging reconstructions. The findings indicate that up to 5x acceleration is possible by a combined compressed sensing and parallel imaging reconstruction. However, efficacy of compressed sensing reconstructions as well as the improvement in image quality over the more conventional parallel imaging and low-resolution acquisitions appear to vary with pulse sequence.Conclusion: Mild to moderate accelerations are possible for those sequences by a combined compressed sensing and parallel imaging reconstruction while maintaining diagnostic quality of reconstructions. Nevertheless, for certain sequences/applications one might mildly reduce the acquisition time by appropriately reducing the imaging resolution while maintaining diagnostic quality/accuracy, rather than the more complicated compressed sensing reconstruction.

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“…These reconstruction algorithms are generally in the state-of-the-art compressive sensing (CS) framework, utilizing prior knowledge effectively and permitting accurate and stable reconstruction from a more limited amount of raw data than requested by the classic Shannon sampling theory. CS-inspired reconstruction algorithms can be roughly categorized into the following stages (Wang et al , 2011): (1) The 1st stage: Candes’ total variation (TV) minimization method and variants (initially used for MRI and later on tried out for CT) (Li and Santosa, ’96; Jonsson et al , ’98; Candes and Tao, 2005; Landi and Piccolomini, 2005; Yu et al , 2005; Candes et al , 2006, 2008; Block et al , 2007; Landi et al , 2008; Sidky and Pan, 2008; Yu and Wang, 2009); (2) the 2nd stage: Soft-thresholding method adapted for X-ray CT to guarantee the convergence (Daubechies et al , 2004; Yu and Wang, 2010; Liu et al , 2011; Yu et al , 2011); and (3) the 3rd stage: Dictionary learning (DL) and non-local mean methods being actively developed by our group and others (Kreutz-Delgado et al , 2003; Gao et al , 2011; Lu et al , 2012; Xu et al , 2012; Zhao et al , 2012a,b). …”

Section: Introductionmentioning

confidence: 99%

Issue Information

Liu

Verbridge

et al. 2014

Scanning

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Summary Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

Cited by 4,162 publications

References 45 publications

Blind motion deblurring from a single image using sparse approximation

Blind motion deblurring from a single image using sparse approximation

Diagnostic quality assessment of compressed sensing accelerated magnetic resonance neuroimaging

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