Dictionary Learning Algorithm Based On TL₁ Norm Penalty

Abstract:In recent years,the use of training data to learn a over-complete dictionary,constructing a versatile,efficient and simple dictionary has become a research hotspot in the field of information.In order to improve the dictionary training speed and performance,this paper replaced the₀Lnorm with the?Transformed₁L Penalty?TL₁ norm in the sparse coding stage and improved the K-SVD dictionary learning algorithm.Aiming at the disadvantages of the large amount of computation and the inherent structure of the destruction training data in the current dictionary learning algorithm,a fast and efficient dictionary learning algorithm based onTL₁ norm penalty is proposed.The main work is as follows:Firstly,when K-SVD dictionary learning algorithm is applied to image reconstruction,the running speed is slow,and the accuracy of recovery is not high enough.In order to improve the dictionary training speed and performance,the non-convex functionTL₁norm is used to replace theL₀ norm in the sparse coding stage,and the iterative threshold algorithm is used to solve the sparse representation.Numerical experiments show that the improved algorithm can get the training dictionary faster than the K-SVD algorithm,get higher peak signal noise,and has good reconstruction performance.Secondly,aiming at the shortages of large amount of calculation and destroying the inherent structure of training data in commonly used dictionary learning algorithms,a fast and efficient dictionary learning algorithm based onTL₁ norm penalty is proposed.First,a special segmentation tree is designed based on principal component analysis and K mean value algorithm classify training data.Second,based on the tree structure to construct an over-complete dictionary.By constructing the dictionary in two steps,the computational load is reduced and the training speed is accelerated.In the model of the dictionary learning,the regularization term of the graph is added to describe the inherent geometric structure of the training data;theTL₁ norm is used to solve the training data to represent the sparseness in the over-complete dictionary.The proposed algorithm is applied to image de-noising.Experimental results show that this algorithm improves the speed of dictionary learning and can get better de-noising results.Compared with other existing methods,this method achieves de-noising effect and computation time significant improvements.