Dictionary Learning Algorithms for Sparse Representation

Kreutz-Delgado, Kenneth; Murray, Joseph F.; Rao, Bhaskar D.; Engan, Kjersti; Lee, Te-Won; Sejnowski, Terrence J.

doi:10.1162/089976603762552951

Cited by 707 publications

(450 citation statements)

References 40 publications

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“…As per the dictionary that leads to sparse decomposition, although working with pre-defined dictionaries may be simple and fast, their performance might be not good for every task, due to their global-adaptivity nature [49]. Instead, learned dictionaries are adaptive to both the signals and the processing task at hand, thus resulting in a far better performance [50].…”

Section: Sparse Image Representationmentioning

confidence: 99%

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

et al. 2018

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Bleed-through is a frequent, pervasive degradation in ancient manuscripts, which is caused by ink seeped from the opposite side of the sheet. Bleed-through, appearing as an extra interfering text, hinders document readability and makes it difficult to decipher the information contents. Digital image restoration techniques have been successfully employed to remove or significantly reduce this distortion. This paper proposes a two-step restoration method for documents affected by bleed-through, exploiting information from the recto and verso images. First, the bleed-through pixels are identified, based on a non-stationary, linear model of the two texts overlapped in the recto-verso pair. In the second step, a dictionary learning-based sparse image inpainting technique, with non-local patch grouping, is used to reconstruct the bleed-through-contaminated image information. An overcomplete sparse dictionary is learned from the bleed-through-free image patches, which is then used to estimate a befitting fill-in for the identified bleed-through pixels. The non-local patch similarity is employed in the sparse reconstruction of each patch, to enforce the local similarity. Thanks to the intrinsic image sparsity and non-local patch similarity, the natural texture of the background is well reproduced in the bleed-through areas, and even a possible overestimation of the bleed through pixels is effectively corrected, so that the original appearance of the document is preserved. We evaluate the performance of the proposed method on the images of a popular database of ancient documents, and the results validate the performance of the proposed method compared to the state of the art.

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Section: Sparse Image Representationmentioning

confidence: 99%

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

et al. 2018

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“…The minimum norm solution has the tendency to spread the energy rather than obtaining sparse solution (15,16). To derive FOCUSS, let us consider the following optimization problem: find x = Wq, [5] where x is the unknown image, W is a weighting matrix, and q is computed from the following constrained minimization problem:…”

Section: Review Of Focussmentioning

confidence: 99%

“…The main contribution of this article is to demonstrate that a new type of sparse reconstruction algorithm called the focal underdetermined system solver (FOCUSS) (14)(15)(16) is suitable for projection reconstruction MR imaging. FOCUSS was originally designed for electroencephalogram (EEG) and magnetoencephalography (MEG) source localization problems by obtaining sparse solutions from successive quadratic optimization problems (14,15).…”

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confidence: 99%

Projection reconstruction MR imaging using FOCUSS

Tak

Han

et al. 2007

Magnetic Resonance in Med

105

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The focal underdetermined system solver (FOCUSS) was originally designed to obtain sparse solutions by successively solving quadratic optimization problems. This article adapts FOCUSS for a projection reconstruction MR imaging problem to obtain high resolution reconstructions from angular undersampled radial k -space data. We show that FOCUSS is effective for projection reconstruction MRI, since medical images are usually sparse in some sense and the center region of the undersampled radial k -space samples still provides a low resolution, yet meaningful, image essential for the convergence of FOCUSS. Projection reconstruction (PR) with radial k-space trajectory was the first MRI k-space trajectory in MR history (1). However, cartesian k-space trajectory has replaced PR, mainly because of artifacts of PR that are related to B 0 inhomogeneity and to gradient nonlinearity (2). However, recent advances in MR hardware technology have overcome problems related to B 0 inhomogeneity and gradient nonlinearity, and interest in PR has thus been revived. PR has many advantages over the conventional cartesian k-space trajectory (3). Since no phase-encoding gradient is used, PR has a shorter minimum TE, which has made PR particularly desirable for imaging very short T 2 nuclei (3-5). Another advantage of PR is its robustness to the motion artifacts from flow or respiration. One important example is the reduction of motion artifacts in a diffusionweighted MRI (6,7). Furthermore, the aliasing artifacts from radial under-sampling usually appear as streaks, which are visually less distracting than the wrap-around artifacts obtained with cartesian under-sampling.One of the disadvantages of PR is the increased scan time involved if the Nyquist sampling criterion needs to be satisfied. More specifically, the number of radial lines N s required to satisfy the Nyquist criterion is given by (3):where L is the field-of-view (FOV), and k max is the maximum k-space radius. Usually, the number of radial lines acquired by PR is about 57% larger than the number of k-space lines acquired on a cartesian grid, which results in the increased scan time (3). If streak aliasing artifacts can be tolerated in an application, the scan time can be reduced by using angular undersampling. One such undersampled PR application is contrast-enhanced vascular imaging (8).Because of the properties of PR, if the contrast enhanced vessels are located at the center of the FOV, the undersampling aliasing artifacts appear as streaks near the periphery of the FOV and usually do not interfere with vessels located at the center of FOV. Hence, this application of PR for angiography has been a success (8).Rather than tolerating the angular aliasing artifacts, however, the main goal of our research is to develop a novel reconstruction algorithm with minimal angular aliasing. The bases of such a novel algorithm are the following two observations: (a) most medical imaging is sparse in some sense, and (b) the under-sampled PR still provides a meaningful low resolution imag...

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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%

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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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Dictionary Learning Algorithms for Sparse Representation

Cited by 707 publications

References 40 publications

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

Projection reconstruction MR imaging using FOCUSS

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