Dictionaries for Sparse Representation Modeling

Rubinstein, Ron; Bruckstein, Alfred M.; Elad, Michael

doi:10.1109/jproc.2010.2040551

Cited by 1,151 publications

(688 citation statements)

References 90 publications

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“…Structured and parametric dictionaries have recently been considered with increasing interest. Interested readers can find a concise bibliographical note on that subject in [19]. In particular, the structures studied so far include unions of orthobases [9], translation invariant dictionaries [11], dictionaries composed of patches with multiple sizes [14], dictionaries divided in ordered pieces (that are learnt from the residuals obtained when representing the sample patches with the previously computed atoms of the dictionary) [24], structures induced by structured codes [7,8].…”

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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Section: Related Workmentioning

confidence: 99%

Toward Fast Transform Learning

Chabiron

Malgouyres²,

Tourneret³

et al. 2014

Int J Comput Vis

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show abstract

“…Many dictionary learning methods have been proposed for image processing [13][14][32][33] and pattern recognition [15-16, 34, 49] where D i is the class-specified sub-dictionary associated with class i. The dictionary D is learned from the training dataset A.…”

Section: Dictionary Learningmentioning

confidence: 99%

“…(12) and the weight w in Eq. (14). Among these parameters, λ 1 and λ 2 are related to dictionary learning, and w is related to the distance measurement.…”

Section: Parameter Selectionmentioning

confidence: 99%

Fast and robust face recognition via coding residual map learning based adaptive masking

Yang

Feng

Shiu

et al. 2014

Pattern Recognition

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“…The central challenge for CS is the construction of preferably non-adaptive relatively small number of linear measurements that can guarantee the reconstruction of a sparse or approximately sparse signal. Such a set of linear measurements are represented by rows of an over complete dictionary, [11], i.e. an mxn matrix whose columns form a spanning set of m-dimensional vectors to be used to decompose the signal.…”

Section: Compressive Sensingmentioning

confidence: 99%

Face Recognition from Degraded Images – Super Resolution Approach by Non-adaptive Image-Independent Compressive Sensing Dictionaries

Jassim

2013

Communications and Multimedia Security

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Abstract. In recent years, the emergence of the new paradigm of compressive sensing (CS) has led to the development of innovative image/signal processing and analysis tools that can be exploited to efficiently deal with serious challenges in pattern recognitions. This paper is concerned with the use of CS tools and dictionaries for face recognition, and in particular when dealing with uncontrolled conditions, e.g. faces captured at a distance in surveillance scenarios or in post-rioting forensic, whereby the images are severely degraded/blurred and of low-resolution. We present the results of our recent investigations 1 into the construction of over-complete dictionaries that recover super-resolved face images from any input low-resolution degraded face image. These results demonstrate that non-adaptive image-independent implicitly designed dictionaries that guarantee the recovery of sparse signals achieve face recognition accuracy levels and yield significant recognition rates that are as good as if not better than those achieved by a recently proposed image-based learnt dictionaries. We shall also show that a variety of random dictionaries known to satisfy the Restricted Isometry Property (RIP), achieve similar accuracy rates, and thereby removing the need for training images. The high quality of the super-resolved images provides great potential for forensics and crime/terrorism fighting.

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Dictionaries for Sparse Representation Modeling

Cited by 1,151 publications

References 90 publications

Toward Fast Transform Learning

Toward Fast Transform Learning

Fast and robust face recognition via coding residual map learning based adaptive masking

Face Recognition from Degraded Images – Super Resolution Approach by Non-adaptive Image-Independent Compressive Sensing Dictionaries

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