Research On Group Sparse Representation Algorithms And Applications

In recent years,compressed sensing has attracted considerable attention in areas of applied mathematics,computer science,electrical engineering and others fields.This has caused great attention,is likely to go beyond the traditional sampling theorem.Compressed sensing is based on the fundamental fact that we can represent many signals using only little non-zero coefficients in a suitable basis or dictionary.In the whole process of compressed sensing,there are the sparse representation of the signal,the design of the observation matrix,and the signal reconstruction.In real life,sparse signals are often not common.Looking for a suitable set of base,become aspect of essential.Often using some standard orthogonal transform,or using the appropriate redundancy dictionary.The design of the observation matrix,meet the Restricted Isometry Property constraints.The signal reconstruction algorithm is diverse,often can be divided into two categories,one greedy algorithm,mainly matching tracking algorithm.The other is a loose convex optimization algorithm,often with a 1l norm to constrain sparse items.Based on above theory,the main contributions of this paper are as follows:(1)We propose an algorithm so called group alternating direction method to solve the group sparse optimization.This paper joins the thought of grouping according to the practical applications.That is,in some applications,the signal is often not only sparse,but also group sparse characteristic.Taking advantage of this feature,we carry out sparse signal grouping.The distance between the group and the group is as large as possible,and the intra-group distance is as small as possible.Our algorithm can be easily implemented in parallel computing,which provides a faster and more efficient solution for large-scale data processing.(2)In sparse representation based classifier,we propose group sparse representation based classifier algorithm.Take into consideration the dictionary matrix of face images,have the features of group sparse,the result will be better using the group idea.And Firstly for the test image,we calculate the weight with dictionary matrix,then calculate the group sparse representation of dictionary according to group alternating direction multiplier method.Finally,we do face recognition.On the recognition rate and running time,the algorithm performance is very competitive.(3)In the field of simulated experiments,there are two kinds of experiments,one of which was the experiment of the compressed sensing reconstruction algorithm.This includes reconstruction of simulated data and reconstruction of real images.The second type is a sparse group of face recognition algorithm.This article is conducted on the YaleB database.Our algorithm is very competitive in simulated data recovery and the effect of face recognition.