Subset pursuit for analysis dictionary learning

Most existing analysis dictionary learning (ADL) algorithms, such as the Analysis K-SVD, assume that the original signals are known or can be correctly estimated. Usually the signals are unknown and need to be estimated from its noisy versions with some computational efforts. When the noise level is high, estimation of the signals becomes unreliable. In this paper, a simple but effective ADL algorithm is proposed, where we directly employ the observed data to compute the approximate analysis sparse representation of the original signals. This eliminates the need for estimating the original signals as otherwise required in the Analysis K-SVD. The analysis sparse representation can be exploited to assign the observed data into multiple subsets, which are then used for updating the analysis dictionary. Experiments on synthetic data and natural image denoising demonstrate its advantage over the baseline algorithm, Analysis K-SVD.