Sparse signal decomposition and representation have always served as the cornerstone of any highperformingsignal processing algorithm. A sparse representation not only provides better signalcompression for bandwidth efficiency, but also leads to faster processing algorithms as well as more effective signal separation for detection, classification, and recognition purposes. Sparse signal representation allows us to capture the simple structure often hidden in visual data, and thus minimizes the undesirable effects of noise in practical settings. Fortunately, most natural signals encountered in practice, especially highly-correlated images and video sequences, are inherently sparse. However, such signals are also highly non-stationary as well. Optimal prediction, sampling, representation,and estimation of these signals require locally-adaptive decomposition and/or representation that can quickly capture the signal characteristics within a small local neighborhood of interest.

In this project, we have addressed three critical drawbacks in current sparse recovery approaches: (i) the lack of local adaptivity to effectively deal with highly non-stationary signals; (ii) rich spatiotemporal correlation structure often existing in natural signals has not been fully taken into account; (iii) the associatednon-trivial level of computational complexity and robustness issues in large-scale practical applications.

We have demonstrated the effectiveness of our approach in two major application areas. In reconstruction applications such as image/video denoising, enhancement, and error-concealment, recovery accuracy is greatly improved by taking into account inter-patch spatial correlation, inter-frame temporal correlation, and by adapting algorithms dynamically based on local signal contents. In the particular application of video concealment over lossy packet networks (especially in the very challenging scenarios with 50%-75% packet loss), our approach gains an average of 5 dB improvement over the boundary-matching algorithm employed in many international video coding standards.

In discrimination applications such as target/pattern detection, classification, and recognition, higher-quality recovery partially helps but it is not the ultimate deciding factor. We have concentrated our effort on maximizing the level of discrimination within the sparse recovery process to obtain optimal algorithmic performances. Particularly, we exploit strong correlation between local features and capture connections between these different features with discriminative graphical models. We also explore discriminative online dictionary learning and kernelized high-dimensional sparse-representations to improve sparsity-based classification approaches.

In summary, this project provides several significant contributions with profound potential impacts, especially in sparsity-driven signal processing applications. To the best of our knowledge, results obtained in this effort – from video concealment to robust face recognition to hyper-spectral target detection – offer state-of-the-art levels of performance. Our adaptive concealment/denoising scheme via tensor completion pushes the frontier in video communications over unreliable time-varying wireless channels. Sparsity-driven techniques in classic detection, classification, and recognition are expected to have a major impact in enhancing and aiding critical monitoring applications for national security, fromborder surveillance to airport security. Similar techniques applied to medical imaging can improve the quality and reduce the cost of health care. Our research not only provides new tools for but also deepens our understanding of principal component signal analysis, sparse signal representation, adaptive signal modeling, and efficient data collection – all of which are common tools in ma...

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