Learning Multilevel Dictionaries for Compressed Sensing Using Discriminative Clustering

The performance of sparse recovery using compressed measurements improves when dictionaries learned from training data are used in place of predefined dictionaries. In this paper, we propose to learn incoherent multilevel dictionaries using discriminative clustering in each level. To this end, we present the discriminative K-lines clustering that iterates between identifying the cluster centers and computing the discriminant directions. A scheme for computing representations using the proposed dictionary is also developed. Simulation results for compressed sensing using standard images demonstrate that incorporating incoherence in the dictionary results in improved recovery performance. Furthermore, we implement the proposed algorithms as part of a sparse representations toolbox for the J-DSP software package.