Research On The Sparse Reconstruction Algorithm Based On Adaptive Dictionary Learning

In sparse representation theory,in order to achieve the sparse representation of signals,a set of given training signal can be represented by a linear combination of a small number of dictionary atoms when a over-complete dictionary containing the information of given signal is used.Redundant dictionary can be generated by defining a fixed base,or can be obtained by learning some algorithm.In recent years,a learning dictionary is a research hotspot,which can adaptive the basis function according to the structure of the training sample,and can more accurately extract the signal structure characteristics.However,the fixed base dictionary can't adaptive signal structure characteristics,and the sparse reconstruction error of which is more than the learning dictionary.An improvement of K-SVD dictionary learning algorithm has been proposed in this paper,through the two-stage iteration of sparse coding and dictionary update.In order to improve the dictionary training speed and performance,Augmented Lagrangian multiplier method(ALM)is introduced in the sparse coding stage,while the standard K-SVD dictionary updating algorithm is used in the dictionary update stage.In this work,the dictionary training speed and root-mean-square error(RMSE)of the algorithm are investigated in the synthesis date experiment by selecting different sample sets and noise standards.The results show that the algorithm is better than the standard K-SVD dictionary learning,which receives faster training speed and lower RMSE.In order to investigate the image denoising ability of the algorithm,simulation experiment is carried out by selecting different input image noise standards and the atomic numbers of the dictionary.The algorithm shows higher peak signal-to-noise ratio(PSNR)and better denoising performance than the standard K-SVD algorithm.