Applications of Sparse Representation, Low Rank Approximation and Dictionary Learning to Image Processing, Pattern Recognition and Computer Vision

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Human vision is good at detecting objects such as human faces under various conditions: illumination, occlusions, and poses. Training the computer to mimic human vision has occupied scientists and engineers for many years. One of the major problems is dealing with very large amount of image data. Since images such as human faces or video frames can be stored in large matrices or tensors, the research in large scale data analysis for matrices and tensors has become a hot topic. In particular, techniques such as sparse representation, low rank approximation, dictionary learning, robust principal component analysis, and multi-linear principal component analysis have brought much attention and are powerful tools in image/video processing, pattern recognition and computer vision. A common problem among these techniques is the need for efficient computational methods for optimizing the related objective functions. An efficient optimization technique will lead to a significant reduction in computational costs as well as an improvement on accuracy of the solutions. Furthermore, real data sets are often incomplete with many dimensions or elements missing. They may contain corrupted information due to measurement or communication errors. Hence the analysis of large data sets coming from real-world problems has been one of the most challenging tasks. As an example, in biometrics, face recognition under a combined effect of illumination, resolution, orientation, expression, and occlusion has been one of the major problems in computer vision. The objective of this research is to develop models and solution methods that can be applied to the problems mentioned above and common mathematical problems will be investigated. Specifically we are concerned with three main issues: (1) Development of common models and frameworks for the analysis of large scale image datasets; (2) Analysis of different factors that affect the systems such as the choice of input data for training, and the limitation of the proposed techniques; and (3) Implementation, experimentation and testing of the new models and techniques. The proposed work can have significant impact on many areas including image/video processing, computer vision, security, biometrics, telecommunications, remote sensing, and bioinformatics. One of the applications of our work is on face age progression that can be useful for the investigation of missing children.