Parallel Mri Reconstruction Using Svd-and- Laplacian Transform Based Sparsity Regularization

The SENSE model with sparsity regularization acts as an unconstrained minimization problem to reconstruct the MRI, which obtain better reconstruction results than the traditional SENSE. To implement the sparsity constraints, discrete wavelet transform (DWT) and total variation (TV) are common exploited together to sparsify the MR image. In this paper, a novel sparsifying transform based on the combination of singular value decomposition (SVD) and Laplacian (LP) transform is proposed for parallel MR image reconstruction. The proposed algorithm adopts the SVD of the MR image as sparsifying transform instead of exploiting the wavelet domain sparsity of the image, and uses the LP-norm as an alternative to TV-norm in the sparsity regularization term. The performances of the proposed method are evaluated on two typical types of MR image (complex brain MR image and sparse angiogram MR image). Compared with the DWT-TV sparsifying transform, the proposed SVD-LP method can significantly achieve better reconstruction quality and considerably improve the computation efficiency.