ABSTRACTDISCRIMINATIVE SPARSE REPRESENTATIONS FOR IMAGE CLASSIFICATIONBySuhaily Cardona-Romero Sparse representations and compressed sensing (CS) are two methods that have drawn the attention of the signal processing community due to their ability to reduce the dimensionality of signals while preserving enough information for signal representation. However, these compact representations do not necessarily preserve the most discriminative aspects of the signal. This thesis addresses this issue by developing a new discriminative framework to obtain a compact representation with high discriminative information for image classification applications. The first part of this thesis presents a greedy algorithm inspired by CoSaMP with the inclusion of a new cost function that quantifies the tradeoff between discrimination power and sparsity. The inclusion of this cost function helps to select a small number of atoms from an overcomplete dictionary that produces discriminative sparse representations of images from different classes. Through experiments, it was shown that such representations can be used as features to classify new sample images even under noisy environments or missing pixels. The second part of this thesis proposes a method to obtain discriminative measurements from CS and is motivated by the fact that the presence of irrelevant features may reduce the classification accuracy. To address this issue, a feature selection step was added to CS to eliminate irrelevant features from the measurements. As a result of the elimination of such features, an improvement in the classification accuracy is observed. In conclusion, it was demonstrated that a subset of incoherent projections with high discrimination power performs better than the whole set of CS measurements for classification purposes.
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