Sparse Representation And Reconstruction Method Of Image Signal Based On Compressed Sensing

Traditional image signal processing is based on the Nyquist sampling theorem, which requiresthat the sampling rate of the signal be greater than or equal to twice the highest frequency of thesignal. This sampling will usually generate a large amount of redundant information, and thusimpose a great pressure on image storage, processing and transmission. Due to the bottleneck ofNyquist sampling theorem, a new sampling algorithm called compressed sensing has been proposed.The research on compressed sensing theory includes three parts: sparse representation of imagesignal, observation matrix design and image reconstruction algorithm. This thesis first studies thesparse representation and reconstruction algorithm. A practical image reconstruction model then isproposed for the application of image reconstruction. The main contributions of the thesis aresummarized as follows:(1) Considering that traditional dictionary learning algorithm can not exploit the detailedinformation of original image, this thesis proposes a new K-SVD method for training the classifiedtraining data. Experimental results show that the new training method has a better performance thanthe traditional training algorithms does.(2) A fast OMP algorithm is proposed through analyzing three existing greedy matching pursuitalgorithms. The proposed reconstruction algorithm makes use of hard threshold to accelerate thereconstruction speed. The experiments have confirmed the good performance of the proposedreconstruction algorithm.(3)An adaptive image reconstruction model is proposed for the implementation of the newK-SVD training method. The new model has two advantages:1) The sampling rate of the proposedreconstruction model can be allocated adaptively according to the amount of information indifferent image blocks.2) It successfully incorporates the new proposed sparse dictionary into theimage reconstruction model. Experimental results show that the proposed adaptive imagereconstruction model can completely keep the image edges and details.