The Research Of Compressive Sensing Reconstruction Algorithm

The classical Nyquist theorem says that if the rate for sampling a signal is at least twice the bandwidth of its frequency, signal can be reconstructed without distortion. However, with the rapid development of information techniques, the amount of data to be handled is increased and signals'bandwidth is becoming wider. There is no doubt that the ability of signal processing should be strengthened and hardware devices are under more pressure. In 2006, Donoho and Candes proposed a theory called compressive sensing (CS), which can solve the problems above. When signals are sparse in themselves or in some special transform domains, CS manages to compress signals by means of incoherent measurements with proper measurement matrices. Signals can be reconstructed with high probability from only a few observations with optimization algorithms.Based on the researches of the existed reconstruction algorithms, the paper proposes a new algorithm TV1 to solve the existed total variation minimization problem and modifies the total variation model, then proposes a new algorithm TV2 to solve the modified total variation minimization problem.Firstly, the paper classified and summarized the existed CS reconstruction algorithms which can't recover images'edges and texture ideally. A new algorithm called TV1 is proposed. TV1 utilized the existed TV model, which makes use of the characteristic that adjacent pixels'values of images are similar. TV1 uses Walsh-Hadamard transform matrix as sampling matrix, in order to improve the algorithm convergence speed. Experimental results show the proposed method has a better reconstruction result and a faster convergence rate than the existed algorithms.Secondly, total variation simply uses the local smooth priors of images, and ignores the sparse priors of images in transform domains. Therefore, the paper adds a new constraint to the TV model and uses a new algorithm TV2 to solve it. The new constraint utilizes images'sparsity in Contourlet domain. TV2 can improve images'reconstruction quality by removing irrelevant vectors from the feasible set of the optimization problem. Experimental results show that compared with TV1, TV2 performs better.