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).
Recursive Least Squares Dictionary Learning Algorithm
We present the recursive least squares dictionary learning algorithm, RLS-DLA, which can be used for learning overcomplete dictionaries for sparse signal representation. Most DLAs presented earlier, for example ILS-DLA and K-SVD, update the dictionary after a batch of training vectors has been processed, usually using the whole set of training vectors as one batch. The training set is used iteratively to gradually improve the dictionary. The approach in RLS-DLA is a continuous update of the dictionary as each training vector is being processed. The core of the algorithm is compact and can be effectively implemented. The algorithm is derived very much along the same path as the recursive least squares (RLS) algorithm for adaptive filtering. Thus, as in RLS, a forgetting factor ¿ can be introduced and easily implemented in the algorithm. Adjusting ¿ in an appropriate way makes the algorithm less dependent on the initial dictionary and it improves both convergence properties of RLS-DLA as well as the representation ability of the resulting dictionary. Two sets of experiments are done to test different methods for learning dictionaries. The goal of the first set is to explore some basic properties of the algorithm in a simple setup, and for the second set it is the reconstruction of a true underlying dictionary. The first experiment confirms the conjectural properties from the derivation part, while the second demonstrates excellent performance.
Online Robust Non-negative Dictionary Learning for Visual Tracking
This paper studies the visual tracking problem in video sequences and presents a novel robust sparse tracker under the particle filter framework. In particular, we propose an online robust non-negative dictionary learning algorithm for updating the object templates so that each learned template can capture a distinctive aspect of the tracked object. Another appealing property of this approach is that it can automatically detect and reject the occlusion and cluttered background in a principled way. In addition, we propose a new particle representation formulation using the Huber loss function. The advantage is that it can yield robust estimation without using trivial templates adopted by previous sparse trackers, leading to faster computation. We also reveal the equivalence between this new formulation and the previous one which uses trivial templates. The proposed tracker is empirically compared with state-of-the-art trackers on some challenging video sequences. Both quantitative and qualitative comparisons show that our proposed tracker is superior and more stable.
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