The Study On Fast Magnetic Imaging Reconstruction By Using Total Variation Based Sparsity Constraint

The principle of Nyquist has been a bottleneck for big data collection, compression and transmission. Recently, with the advent of sparse MRI, such a bottleneck problem seems to be solved in some degree. The sparse MRI indicates that, if the sampling of the image is random undersampling, and the artifacts caused by random undersampling has a similar performance like the noise, then the under-sampled image can be reconstructed accurately by an appropriate nonlinear algorithm when the image is sparse in its transform domain.Based on this idea, this paper puts forward a new reconstruction method, called Group-Sparsity Total Variation (GSTV), which is implemented by combining group sparsity with the shift-invariant discrete wavelet transform (SIDWT) and fast composite splitting algorithm (FCSA). The main researches are included as following:(1) Sparse constraint is very important for reconstructing the under-sampled MR images. The original images can be reconstructed by solving the quadratic optimization problem from the prior knowledge of sparsity and the observed values. In this paper, total variation has been used as the sparsity constraint, and applies it to MRI reconstruction. From the results, one can find that Total Variation (TV) method can reconstruct the MR images but results in the staircase effects. Some extensions of total variation, i.e. High Degree TV (HDTV) method and Total Generalized Variation (TGV) method, have been discussed in this paper, which can remove the staircase effects and perform well on the MR imaging reconstruction.(2) In this paper, the Group-Sparse Total Variation (GSTV) method has been applied to MR images reconstruction, which can be achieved by the sparse regularization model. Based on the wavelet transform and sparse matrix, the mathematical model is consisted by the least square fitting data, sparse combination of total variation regularization model of sparse regularization term and L1 norm regularization term. And Fast Composite Splitting Algorithm (FCSA) method is employed to solve the above problem. The experimental results show that the GSTV method outperforms the other methods in terms of denoising and reconstruction, providing an effective alternative solution to the reconstruction framework.