Algorithm for sparse representation minimizing mean square error of power spectrograms

Sparse representation is an idea to approximate a target signal by a linear combination of a small number of sample signals, and it is utilized in various research fields. In this paper, we evaluate the approximation error of signals by the mean square error of power spectrograms (P-MSE). Specifically, we propose a P-MSE minimization algorithm for sparse representation. Our method minimizes the P-MSE by an iterative approach. Specifically, in each iteration, we find the optimal sample signal and optimize the corresponding coefficients by a gradient-based method. In this approach, our method can utilize the result of the previous iteration for fast and stable convergence in the optimization of the coefficients. Based on this algorithm, the sparse representation which minimizes the P-MSE becomes feasible. Experimental results show the effectiveness of our method in terms of the P-MSE minimization.