Research On Reconstruction Algorithm Of Compressed Sensing

Compressed Sensing(CS)is a novel sampling theory that breaks from the traditional Nyquist sampling theorem by sampling signals in a much more efficient way.CS has recently gained a lot of attention due to the exploration of sparse signal.When a signal is sparse or compressible,it can be accurately reconstructed by non-linear reconstruction algorithms via a few measurements.Therefore,it can save shortage space and time.Reconstruction algorithms are one of the key parts of CS,and they solve the problem of how to reconstruct the original high dimensional data from low dimensional data.The matching pursuit(MP)-family algorithms have better reconstruction performs,so they are widely used.This paper studies the MP-family algorithms in view of reconstruction accuracy and reconstruction time,and attempts to improve and apply some of them.Specific research works include the following aspects:(1)Analysis of SP algorithm processes,which requires knowing prior sparsity information.Furthermore,it sometimes selects the wrong atoms in the process of backtracking.To solve these problems,we use a new soft method to obtain the signals sparsity and adopt a week selection to select the atoms when backtracking,which improves the performance of the SP algorithm.Experimental results showed that the proposed algorithm has a higher reconstruction accuracy and lower reconstruction time.(2)In order to optimize the performance of the SAMP algorithm,a new Improved Sparsity Adaptive Matching Pursuit(ISAMP)algorithm is proposed.The proposed algorithm introduces generalized Dice coefficient for matching criterion,which improves its performance in selecting the most matching atom from a measurement matrix for residual signal.Meanwhile,It uses a threshold method to select preliminary set and adopts exponential variable steps during the iteration,using a large step to enhance the execution efficiency at the original stage.When the estimated sparsity is closed to the true sparsity,we use decreasing step size to improve the reconstruction accuracy.Experimental results show that the proposed algorithm improves SAMP algorithm both in reconstruction quality and computational time.(3)The OMP algorithm is used as the sparse decomposition algorithm in image sparse representation,combining with the advantages of sparse representation and nonlinear diffusion method.Thereby,a new image multiplicative denoising model is established.Sparse representation over SGK algorithm has shown its usability and quick execution forimage recovery and are able to recover textures efficiently and accurately.The nonlinear diffusion regularization is beneficial for preserving the edge of an image.We use three steps to solve the complex model: First,we use the SGK algorithm to train the dictionary and obtain the sparse representation in the log-image.Second,we propose an alternating minimization algorithm to solve the remainder.Finally,we transform the recovered log-image into a real domain.Numerical experiments show that the proposed model preserves both edges and structures while removing multiplicative noise quickly.