This thesis considers an algorithm for classification with outlier rejection using a discriminative dictionary based on non-negative mutual incoherency (DNMI). The dictionary and non-negative coefficients are obtained by minimizing an empirical reconstruction error and mutual coherency among atoms of different classes. The non-negative condition on the coefficients redefines the spanning space of the atoms to encourage a sample of a particular class to be reconstructed by atoms of the same class under the sparsity constraint. For target samples, classification is performed in the similar manner as was used in the LC-KSVD algorithm. Prior to classification, outliers are rejected based on four rejection measures: (1) normalized weighted concentration of the atoms of the most used class, (2) entropy of weighted class concentrations, (3) variance of the coefficients, and (4) reconstruction accuracy.Experimental results on two benchmark image datasets, Caltech101 and Caltech 256, show that the proposed algorithm provides better classification and rejection results than other conventional sparse representation for classification.