Dictionary Learning Algorithms for Sparse Representation
Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial 25 words or less), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error).
Inpainting and Zooming Using Sparse Representations
Representing the image to be inpainted in an appropriate sparse representation dictionary, and combining elements from Bayesian statistics and modern harmonic analysis, we introduce an expectation maximization (EM) algorithm for image inpainting and interpolation. From a statistical point of view, the inpainting/interpolation can be viewed as an estimation problem with missing data. Toward this goal, we propose the idea of using the EM mechanism in a Bayesian framework, where a sparsity promoting prior penalty is imposed on the reconstructed coefficients. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered/interpolated based on sparse representations. We first introduce an easy and efficient sparse-representation-based iterative algorithm for image inpainting. Additionally, we derive its theoretical convergence properties. Compared to its competitors, this algorithm allows a high degree of flexibility to recover different structural components in the image (piecewise smooth, curvilinear, texture, etc.). We also suggest some guidelines to automatically tune the regularization parameter.
Graph-Preserving Sparse Nonnegative Matrix Factorization With Application to Facial Expression Recognition
In this paper, a novel graph-preserving sparse nonnegative matrix factorization (GSNMF) algorithm is proposed for facial expression recognition. The GSNMF algorithm is derived from the original NMF algorithm by exploiting both sparse and graph-preserving properties. The latter may contain the class information of the samples. Therefore, GSNMF can be conducted as an unsupervised or a supervised dimension reduction method. A sparse representation of the facial images is obtained by minimizing the -norm of the basis images. Furthermore, according to the graph embedding theory, the neighborhood of the samples is preserved by retaining the graph structure in the mapped space. The GSNMF decomposition transforms the high-dimensional facial expression images into a locality-preserving subspace with sparse representation. To guarantee convergence, we use the projected gradient method to calculate the nonnegative solution of GSNMF. Experiments are conducted on the JAFFE database and the Cohn-Kanade database with unoccluded and partially occluded facial images. The results show that the GSNMF algorithm provides better facial representations and achieves higher recognition rates than nonnegative matrix factorization. Moreover, GSNMF is also more robust to partial occlusions than other tested methods.
Image inpainting via sparse representation
This paper proposes a novel patch-wise image inpainting algorithm using the image signal sparse representation over a redundant dictionary, which merits in both capabilities to deal with large holes and to preserve image details while taking less risk. Different from all existing works, we consider the problem of image inpainting from the view point of sequential incomplete signal recovery under the assumption that the every image patch admits a sparse representation over a redundant dictionary. To ensure the visually plausibility and consistency constraints between the filled hole and the surroundings, we propose to construct a redundant signal dictionary by directly sampling from the intact source region of current image. Then we sequentially compute the sparse representation for each incomplete patch at the boundary of the hole and recover it until the whole hole is filled. Experimental results show that this approach can efficiently fill in the hole with visually plausible information, and take less risk to introduce unwanted objects or artifacts.
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