Research And It's Application Of Compressing Sensing Reconstruction Method Based On Separable Dictionary

As an efficient data processing technology,compressive sensing has become the researching hotspot in the field of image processing,machine learning and pattern recognition.One of the key points of compressive sensing is the signal reconstruction.However,traditional reconstruction algorithms based on single dictionary always need to transform matrix or matrix block into vector,which not only has lower efficiency,but also destroys the two-dimensional structure.Therefore,it is important to study more efficient reconstruction algorithm.Recently,compressive sensing reconstruction algorithm based on separable dictionary has been paid more attention by researchers.It has better performance in dealing with twodimensional signal than traditional reconstruction algorithm based on single dictionary.However,it still has shortcomings and needs to be further improved.In this paper,focusing on compressive sensing reconstruction algorithms based on separable dictionary,we mainly study the separable dictionary training model based on matrix manifold and the separable dictionary training model based on generalized low rank matrix approximation.The main work is summarized as follows:1.A reconstruction algorithm based on separable dictionary construction with matrix manifold is proposed.In this section,the super linear convergence rate of the matrix manifold is used to construct an efficient separable dictionary,and a fast reconstruction algorithm based on the separable dictionary is designed.The experimental results show that the proposed algorithm has lower reconstruction running time than traditional reconstruction algorithms.Furthermore,it also has better reconstruction quality in most cases.2.A reconstruction algorithm based on the training of separable dictionary by the generalized low rank matrix approximation is proposed.Firstly,a new robust generalized low rank matrix approximation model is constructed.Then,the alternating direction method of multipliers is used to solve this optimization problem.A pair of column orthogonal matrices can be obtained.Finally,the column orthogonal matrices are used as separable dictionary,and a fast reconstruction algorithm is presented.The experimental results show that the proposed algorithm has better reconstruction quality and the lowest running time for training set images,and it also has good performance for other types of images.3.A fabric defect detection method based on the proposed generalized low rank matrix approximation model is proposed.After image preprocessing,the defect detection model based on the generalized low rank matrix approximation model is constructed.The experimental results show that the proposed method can deal with multiple images efficiently at the same time.In addition,for the defection of common fabric defects,such as vertical,horizontal,blocky and oblique,the proposed method has better performance than the defect detection method based on the traditional low rank matrix recovery theory.