Multi-separable dictionary learning

Abstract As the extensive applications of sparse representation, the methods of dictionary learning have received widespread attentions. In this paper, we propose a multi-separable dictionary learning (MSeDiL) algorithm for sparse representation, which is based on the Lagrange Multiplier and the QR decomposition. Different with the traditional dictionary learning methods, the training samples are clustered firstly. Then the separable dictionaries for each cluster are optimized by the QR decomposition. The efficiency of the reconstruction process is improved in our algorithm because of the under-determinedness of the dictionaries for each cluster. Experimental results show that with the similar PSNR (Peak Signal to Noise Ratio) and SSIM (Structure Similarity Index), the reconstruction speed of our algorithm is much faster than other dictionary learning methods, especially when the size of samples is large.