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Sparse Representation For Computer Vision and Pattern Recognition
, 2009
"... Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact highfidelity representation of the observed signal, but also to extract semantic information. The choice of ..."
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Cited by 146 (9 self)
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Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact highfidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining stateoftheart results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.
NonParametric Bayesian Dictionary Learning for Sparse Image Representations
"... Nonparametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this nonparametric method naturally infers ..."
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Cited by 92 (34 self)
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Nonparametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this nonparametric method naturally infers an appropriate dictionary size. The Dirichlet process and a probit stickbreaking process are also considered to exploit structure within an image. The proposed method can learn a sparse dictionary in situ; training images may be exploited if available, but they are not required. Further, the noise variance need not be known, and can be nonstationary. Another virtue of the proposed method is that sequential inference can be readily employed, thereby allowing scaling to large images. Several example results are presented, using both Gibbs and variational Bayesian inference, with comparisons to other stateoftheart approaches.
Exploiting structure in waveletbased Bayesian compressive sensing
, 2009
"... Bayesian compressive sensing (CS) is considered for signals and images that are sparse in a wavelet basis. The statistical structure of the wavelet coefficients is exploited explicitly in the proposed model, and therefore this framework goes beyond simply assuming that the data are compressible in a ..."
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Cited by 91 (14 self)
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Bayesian compressive sensing (CS) is considered for signals and images that are sparse in a wavelet basis. The statistical structure of the wavelet coefficients is exploited explicitly in the proposed model, and therefore this framework goes beyond simply assuming that the data are compressible in a wavelet basis. The structure exploited within the wavelet coefficients is consistent with that used in waveletbased compression algorithms. A hierarchical Bayesian model is constituted, with efficient inference via Markov chain Monte Carlo (MCMC) sampling. The algorithm is fully developed and demonstrated using several natural images, with performance comparisons to many stateoftheart compressivesensing inversion algorithms.
TaskDriven Dictionary Learning
"... Abstract—Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that ..."
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Cited by 86 (3 self)
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Abstract—Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a largescale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in largescale settings, and is well suited to supervised and semisupervised classification, as well as regression tasks for data that admit sparse representations. Index Terms—Basis pursuit, Lasso, dictionary learning, matrix factorization, semisupervised learning, compressed sensing. Ç 1
Bilevel Sparse Coding for Coupled Feature Spaces
"... In this paper, we propose a bilevel sparse coding model for coupled feature spaces, where we aim to learn dictionaries for sparse modeling in both spaces while enforcing some desired relationships between the two signal spaces. We first present our new general sparse coding model that relates signal ..."
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Cited by 17 (1 self)
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In this paper, we propose a bilevel sparse coding model for coupled feature spaces, where we aim to learn dictionaries for sparse modeling in both spaces while enforcing some desired relationships between the two signal spaces. We first present our new general sparse coding model that relates signals from the two spaces by their sparse representations and the corresponding dictionaries. The learning algorithm is formulated as a generic bilevel optimization problem, which is solved by a projected firstorder stochastic gradient descent algorithm. This general sparse coding model can be applied to many specific applications involving coupled feature spaces in computer vision and signal processing. In this work, we tailor our general model to learning dictionaries for compressive sensing recovery and single image superresolution to demonstrate its effectiveness. In both cases, the new sparse coding model remarkably outperforms previous approaches in terms of recovery accuracy. 1.
Sensing Matrix Optimization for BlockSparse Decoding
, 2011
"... Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a welldesigned sensing matrix can reduce the coherence between the atoms of the equivalent dictionary, and as a consequence, reduce ..."
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Cited by 16 (2 self)
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Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a welldesigned sensing matrix can reduce the coherence between the atoms of the equivalent dictionary, and as a consequence, reduce the reconstruction error. In some applications, the signals of interest can be well approximated by a union of a small number of subspaces (e.g., face recognition and motion segmentation). This implies the existence of a dictionary which leads to blocksparse representations. In this work, we propose a framework for sensing matrix design that improves the ability of blocksparse approximation techniques to reconstruct and classify signals. This method is based on minimizing a weighted sum of the interblock coherence and the subblock coherence of the equivalent dictionary. Our experiments show that the proposed algorithm significantly improves signal recovery and classification ability of the BlockOMP algorithm compared to sensing matrix optimization methods that do not employ block structure.
Dictionary Learning for Noisy and Incomplete Hyperspectral Images
, 2011
"... We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelengthdependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering ..."
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Cited by 14 (4 self)
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We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelengthdependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous threedimensional (3D) spatiospectral blocks, of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly (“collaboratively”) to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelengthdependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the moreconventional approach of using an i.i.d. Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.
Separable Dictionary Learning
"... Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to c ..."
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Cited by 10 (6 self)
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Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to capture the global structure of a signal and allow a fast implementation, learned dictionaries often perform better in applications as they are more adapted to the considered class of signals. In imagery, unfortunately, the numerical burden for (i) learning a dictionary and for (ii) employing the dictionary for reconstruction tasks only allows to deal with relatively small image patches that only capture local image information. The approach presented in this paper aims at overcoming these drawbacks by allowing a separable structure on the dictionary throughout the learning process. On the one hand, this permits larger patchsizes for the learning phase, on the other hand, the dictionary is applied efficiently in reconstruction tasks. The learning procedure is based on optimizing over a product of spheres which updates the dictionary as a whole, thus enforces basic dictionary properties such as mutual coherence explicitly during the learning procedure. In the special case where no separable structure is enforced, our method competes with stateoftheart dictionary learning methods like KSVD. 1.