Research On Image Reconstruction Algorithm Based On Compressive Sensing

With the development of modern information technology, in the field of signal collection and processing, the data volume and the speed of transmission are increasing rapidly, and requirement to the performance of hardware system is also increasing, the traditional sampling mode based on Nyquist sampling theorem has been under much restriction, and it has been more and more difficult to meet the demands of practical application. The theory of Compressed Sensing(CS), it finishes the data sampling and compressing together, and then reduces the request of sampling rate, breaks the limit of Shannon sampling theorem, and then receives much attention in theoretical research and engineering practice.This paper gives some idea about greedy iterative algorithms in signal reconstruction algorithms, after the study of compressed sensing theory and existing relative algorithms at home and abroad. The main contributes of this paper are as follows.1. The model of compressive sensing theorem is firstly described. First, the three aspects of compressive sensing are introduced briefly; and then the classification of the main algorithms of signal reconstruction in compressive sensing is introduced.2. A deep research of classical reconstruction algorithms, such as OMP?CoSaMP?SP and SAMP, has been done in this paper, and some comparison is made in many matters, such as peak signal to noise ratio(PSNR)?the run time(t(s))?the relative error and the matching rate and so on. With the performance analysis of the algorithms, some insufficiency of the algorithms has been pointed out, and then some relevant modified approach has been improved in this paper.3. Sparsity Adaptive Subspace Pursuit(SASP) algorithm has been presented in this paper. This algorithm obtains the value of sparsity primarily, and then reconstructs the original signal using subspace pursuit algorithm. SASP gets rid of the dependence on the estimation of sparsity, obtains the accurate value of sparsity, and meanwhile adopts SP algorithm, which imports the thought of backtrack, to recover the original signal. The SP algorithm improves the performance obviously both in the accuracy of reconstruction and running time.4. A Modified Adaptive Matching Pursuit(MAMP) algorithm is proved in this paper. In MAMP, the sparsity K is preliminarily estimated in the choice process of support set, and the condition of stopping iteration is modified, and then, the value of sparsity can be obtained, and the real supporting sets can be selected adaptively. Experimental results show that, MAMP improves the running efficiency of algorithm, and meanwhile improves the quality of signal reconstruction, and therefore MAMP is better than SAMP in the performance of reconstruction.