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The analysis and characterization of imaging patterns is a significant research area with several applications to biomedicine, remote sensing, homeland security, social networking, and numerous other domains. In this paper we study and develop mathematical methods and algorithms for disease diagnosis and tissue characterization. The central hypothesis is that we can predict the occurrence of diseases with a certain level of confidence using supervised learning techniques that we apply to medical imaging datasets that include healthy and diseased subjects. We develop methods for calculation of sparse representations to classify imaging patterns and we explore the advantages of this technique over traditional texture-based classification. We introduce integrative sparse classifier systems that utilize structural block decomposition to address difficulties caused by high dimensionality. We propose likelihood functions for classification and decision tuning strategies. We performed osteoporosis classification experiments on the TCB challenge dataset. TCB contains digital radiographs of the calcaneus trabecular bone of 87 healthy and 87 osteoporotic subjects. The scans of healthy and diseased subjects show little or no visual differences, and their density histograms have significant overlap. We applied 30-fold crossvalidation to evaluate the classification performances of our methods, and compared them to a texture based classification system. Our results show that ensemble sparse representations of imaging patterns provide very good separation between groups of healthy and diseased subjects and perform better than conventional sparse and texture-based techniques.
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