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The principal focus of this thesis is the exploration of sparse structures in a variety of statistical modelling problems. While more comprehensive models can be useful to solve a larger number of problems, its calculation may be ill-posed in most practical instances because of the sparsity of informative features in the data. If this sparse structure can be exploited, the models can often be solved very efficiently. The thesis is composed of four projects. Firstly, feature sparsity is incorporated to improve the performance of support vector machines when there are a lot of noise features present. The second project is about an empirical study on how to construct an optimal cascade structure. The third project involves the design of a progressive, rate-distortionoptimized shape coder by combining zero-tree algorithm with beamlet structure. Finally, the longest run statistics is applied for the detection of a filamentary structure in twodimensional rectangular region. The fundamental ideas of the above projects are common — extract an efficient summary from a large amount of data. The main contributions of this work are to develop and implement novel techniques for the efficient solutions of several dicult problems that arise in statistical signal/image processing.

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