Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation

Rubinstein, Ron; Zibulevsky, Michael; Elad, Michael

doi:10.1109/tsp.2009.2036477

Cited by 547 publications

(401 citation statements)

References 41 publications

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“…Dictionary learning algorithms are often sensitive to the choice of m. The update step can either be sequential (one atom at a time) [51,52], or parallel (all atoms at once) [53,54]. A dictionary with sequential update, although computationally a bit expensive, will generally provide better performance than the parallel update, due to the finer tuning of each dictionary atom.…”

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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“…Other interesting dictionaries are characterized by several layers. Such dictionaries can be constructed as the composition of a fixed transform and learned dictionaries [20,17]. They can also be dictionaries made of two layers based on a sparsifying transform and a sampling matrix (both layers can be learnt by the algorithm investigated in [3]).…”

Section: Related Workmentioning

confidence: 99%

Toward Fast Transform Learning

Chabiron

Malgouyres²,

Tourneret³

et al. 2014

Int J Comput Vis

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The dictionary learning problem aims at finding a dictionary of atoms that best represents an image according to a given objective. The most usual objective consists of representing an image or a class of images sparsely. Most algorithms performing dictionary learning iteratively estimate the dictionary and a sparse representation of images using this dictionary. Dictionary learning has led to many state of the art algorithms in image processing. However, its numerical complexity restricts its use to atoms with a small support since the computations using the constructed dictionaries require too much resources to be deployed for large scale applications.In order to alleviate these issues, this paper introduces a new strategy to learn dictionaries composed of atoms obtained as a composition of K convolutions with S-sparse kernels. The dictionary update step associated with this strategy is a non-convex optimization problem. We reformulate the problem in order to reduce the number of its irrelevant stationary points and introduce a Gauss-Seidel type algorithm, referred to as Alternative Least Square Algorithm, for its resolution. The search space of the considered optimization problem is of dimension KS, which is typically smaller than the size of the target atom and is much smaller than the size of the image. The complexity of the algorithm is linear with regard to the size of the image.Our experiments show that we are able to approximate with a very high accuracy many atoms such as modified DCT, curvelets, sinc functions or cosines when K is large (say K = 10). We also argue empirically that, maybe surprisingly, the algorithm generally converges to a global minimum for large values of K and S.

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“…This model provides adaptivity via modification of the matrix A [16], [11]. First note that Φ(x i ) − Φ(X)A i γ i 2 2 can be kernelized as follows,…”

Section: Non-linear Discriminative Dictionary (Nldd)mentioning

confidence: 99%

“…This update can be computed efficiently by utilizing approximate kernel-KSVD algorithm [16] in the feature space. …”

Section: Dictionary Updatementioning

confidence: 99%

Design of Non-Linear Discriminative Dictionaries for Image Classification

Shrivastava

Nguyen

Patel

et al. 2013

Computer Vision – ACCV 2012

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Abstract. In recent years there has been growing interest in designing dictionaries for image classification. These methods, however, neglect the fact that data of interest often has non-linear structure. Motivated by the fact that this non-linearity can be handled by the kernel trick, we propose learning of dictionaries in the high-dimensional feature space which are simultaneously reconstructive and discriminative. The proposed optimization approach consists of two main stages-coefficient update and dictionary update. We propose a kernel driven simultaneous orthogonal matching pursuit algorithm for the task of sparse coding in the feature space. The dictionary update step is performed using an efficient approximate KSVD algorithm in feature space. Extensive experiments on image classification demonstrate that the proposed non-linear dictionary learning method is robust and can perform significantly better than many competitive discriminative dictionary learning algorithms.

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Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation

Cited by 547 publications

References 41 publications

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

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

Toward Fast Transform Learning

Design of Non-Linear Discriminative Dictionaries for Image Classification

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