Academic&Applied Research On Sparse Image Modeling

In high-dimensional feature space, features often have low-dimensional manifoldstructure. So it is significant to discover and infer this structure. The feature space alsohas characteristic of sparsity, therefore signals from both manifold and sparse modelscan be acquired without information loss using sparse measurements rather than rawdata measurements. This paper sets about the research on sparse modeling withmanifold and sparse representation (SR) techniques to discover the low-intrinsic featurestructure, and finally performs image recognition efficiently. The main academiccontributions include:(1) Presenting Uncorrelated and Discriminative Graph Embedding (UDGE) model.UDGE model constructs two sparse nearest-neighbor graphs, within-class andbetween-class graphs, to make the discriminative projections preserve the intrinsicneighborhood geometry of the within-class samples while enlarging the margins ofbetween-class samples near to the class boundaries. With local scaling factor, UDGEcan well represent the contribution of each sample to the classification, and make amore elastic strategy for sample selection. UDGE efficiently dispenses with apre-specified parameter in comparison with the Linear Graph Embedding (LGE), whichsimplifies the recognition process. Moreover, it can address the small sample sizeproblem and its classification accuracy is not sensitive to neighbor samples size andweight value as well. For effectiveness, UDGE model can reveal more discriminativeinformation comparing with LGE framework model, and discover the sparsity ofintra-pattern more explicitly against the Kernel Graph Embedding (KGE) model.(2) Presenting the Fast Sparse Representation Model (FSRM) for large-scale imagerecognition task. The model is the integration of the Matching Pursuit theory andConvex Relaxation theory, which satisfies the Restricted Isometry Property (RIP)requirement, and provably guarantees the stable convergence of the underdeterminedlinear system being solved. Sparse coefficients are produced through the CompressiveSampling Matching Pursuit (CoSaMP) algorithm and a reduced dictionary is devised,then thel1-norm minimization problem can be reduced from a large and dense linearsystem to a small and sparse one, with which enough sparse vectors in the dictionary areguaranteed to represent the samples discriminatively. Experimental results on compleximage databases show FSRM model achieves significant speed-up and reduces much memory keeping the comparable accuracy in comparison with thel1-Magic solver.(3) The exploration of the relationship between the manifold modeling and the SRmodeling forl1-norm minimization problems. The Unified model for Sparse SuspaceLearning (USSL) learns the sparse projection directions and the subspaces spanned bythem vial1-norm regularization term, which integrates the graph embedding modelwith the Least Absolute Shrinkage and Selection Operator (LASSO) by concept. Thesparse representation models mainly consist of convex relaxation and matching pursuitmodels. The solutions of LASSO problem give rise to the correlation of model selectionand the correlation of algorithmic design between them as well. All in all, the manifoldmodels are connected with SR models via (Dτ). With manifold and SR models beingintegrated or mined suitably, intrinsic distribution regularities of complex data can berepresented robustly.