Abstract:

Redundant dictionary learning is an important part of signal sparse representation theory. The mathematical model of signal sparse representation against the differences among training vectors’ representation errors is firstly established, and according to this model a novel dictionary learning algorithm based on weighted least square is presented. The closed solution of this novel algorithm is derived and the selection of the optimal weighting matrix is also discussed. Secondly, in order to avoid matrix inverse operation in closed solution, the online calculating form is further derived. Training vectors are learned successively and the dictionary is updated whenever a training vector is finished. Moreover, the detailed steps are presented and algorithm’s convergence is analyzed. Finally, simulation results show the theoretic analysis’ validity and the algorithm’s feasibility and effectiveness from both signal sparse representation and recovery of known redundant dictionary.