Study On The Application Of Compressed Sensing In Image Compression

Compressed sensing (CS) is a new method for signal sampling and it strucks down the restriction of traditional Nyquist sampling theory. Different from the traditional one, CS can reconstruct the original signal with a small amount of the signal sampling. CS transforms the original signal to sparse signal in another domain, and then maps randomly it by choosing the appropriate observation matrix. At last the original signal can be reconstructed by solving the underdetermined equations. Compressed sensing theory can be only used to process sparse or compressible signal. There are large amount of redundant in the image, and the redundant can be compressed. This can lead to the application of CS for this kind of image. This paper tries to restore the original image accurately from little image samples obtained by compressed sensing, and to redude the transmission bandwidth and storage.In the paper, the main research content and innovations as follows:(1) It introduces the purpose and significance of our research in the paper, and has a detailed description of research status at home and abroad for compressed sensing theory and image compression technology. And this paper describes the necessity and possibility of image compression and presents two common quality evaluation methods of image. Then this paper introduces the reason of propose compressed sensing theory and its core technology, and has a detailed description of the sparse representation of signals and the requirements of designing observation matrix. Lastly, this paper has a detailed overview of the ideas and features of some compressed sensing reconstruction algorithm.(2) This paper studies several greedy pursuit algorithms with their fundamental and steps, and gives their flowcharts. On this basis of this thesis, a new compressed sensing reconstruction algorithm is proposed:Modify Regularization Adaptive Matching Pursuit (MRAMP) algorithm. And then it compares its reconstruct effects of one-dimensional signal and two-dimensional image with Orthogonal Matching Pursuit (OMP) algorithm, Sparsity Adaptive Matching Pursuit algorithm and Subspace Pursuit algorithm. Simulation results show that MRAMP is faster and more accurate for reconstruction one-dimensional signal, and the reconstructed image quality is better than other algorithms.(3) It has a brief description of OMP algorithm based on single-layer wavelet transform. Based on this basis, MRAMP algorithm based on single-layer wavelet transform is proposed to solve the defects on sparsity and complexity, and then compares its experimental effects with MRAMP algorithm and OMP algorithm based on single-layer wavelet transform. The simulation results verify the proposed algorithm is significantly better than MRAMP algorithm, and slightly better than OMP algorithm based on single-layer wavelet transform.