Research Of Log Regularizer Based Convolutional Transform Learning Algorithm And Its Application

In the field of signal processing,signal representation is one of the most basic problems.The effective representation of signal content is the key of signal processing and the basis of signal application.In the digital information age,people are dealing with massive data infor-mation every day.Finding effective representation of data is the direction of signal processing,especially sparse representation of signal.The core idea of sparse representation field is to rep-resent the original data signal with as few non-zero elements as possible,that is,to efficiently represent the key information of the original target signal data with a small amount of data through sparse coding,reducing the redundancy of signal representation and improving the efficiency of signal processing.Convolutional Transform Learning（CTL）is a new sparse representation method.Com-bining the advantages of unsupervised learning and convolutional neural network,it directly extracts features from original signals by learning a set of translation invariant convolutional kernels in an unsupervised way,and has been proved to have stronger sparse representation performance than traditional sparse representation methods.And compared with the convolu-tional neural network,the convolution transformation learning model obtains the convolution kernel through unsupervised learning,there is no dependence on data label problem,overcome the convolution transform learning in the face of no labels or tags are the bottleneck of data,at the same time by the convolution of nuclear group of regularization constraint its diversity,can be extracted from the input signal is more characteristic of diversity,Avoid similar re-dundancy of feature extraction.However,the sparse constraint methods used by the existing convolutional transform learning algorithm are only based onl₀-norm andl₁-norm:Thel₀-norm achieves the effect of sparse constraint by restricting the number of non-zero elements in the feature,but its solution is a NP-hard optimization problem.Greedy algorithm is usually used to select the local optimal value for approximate solution,so it is difficult to obtain the sparse feature with enough ideal accuracy.Thel₁-norm is the convex relaxation solution ofl₀-norm,and the closed solution can be easily obtained by using the soft threshold method.How-ever,l₁-norm has defects of insufficient thinning and excessive punishment of large elements,which also easily lead to the problem of insufficient accuracy of sparse solutions obtained by the model.In addition,the single-layer convolution transform learning sparse coding model is difficult to effectively extract the deep semantic information of signals from input signals rich in information and complex,and its ability to obtain more discriminative deep sparse features is limited.Therefore,in view of the existing problems in convolution transform learning,this thesis studies the convolution transform learning algorithm and its application.The details are as follows:First of all,aiming at the problem that the existingl₀-norm based andl₁-norm based convolutional transform learnings are not accurate enough to extract sparse features,this thesis proposes alogregularizer based convolutional transform learning algorithm.The non-convexlogregularizer method with strong sparsity and small deviation is used as the sparse constraint of convolutional transform learning to improve the accuracy of sparse feature extraction of convolutional transform learning model.Secondly,to solve the problem that it is difficult to extract the deep information of sig-nals in single-layer convolutional transform learning,this thesis proposes a multi-layerlogconvolutional transform learning framework,which extends the single-layerlogconvolutional transform learning model.The multi-layer sparse coding structure is constructed to extract the deep discriminant and semantically rich features of input signals,and to improve the quality of sparse feature extraction of input signals.Finally,aiming at the nonconvex optimization problem oflogregularizer function,this article uses the proximal difference of convex algorithm to solve and optimize the non-convex optimization problem of the objective function of the model.First,the non-convexlogfunction of the objective function is converted into the combination of two convex functions by the difference of convex algorithm,and then the proximal gradient method is used to solve the non-smooth convex optimization problem,and thelogregularizer based convolutional transform learning algorithm based on the proximal difference of convex algorithm method is developed.The experimental results of feature extraction and classification in several public face image data sets show that the proposedlogregularizer based sparse constraint convolutional transform learning algorithm achieves a breakthrough on the existingl₀-norm based andl₁-norm based convolutional transform learning algorithm in sparse feature extraction accuracy.