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Compressed Sensing MRI via Extended Anisotropic and Isotropic Total Variation

Compressed sensing (CS) is a technique to reconstruct images from undersampling data, reducing the scanning time of magnetic resonance imaging (MRI). It utilizes the sparsity of images in some transform domains. Total variation (TV) has been applied to enforce sparsity. However, traditional
 TV based on the l1-norm is not the most direct way to induce sparsity, and it cannot offer a sufficiently sparse representation. Since the lp-norm (0< p < 1) promotes the sparsity better than that of the l1-norm, we
 propose two extended TV algorithms based on the lp-norm: anisotropic and isotropic total p-variation (TpV). Then we introduce them to the MRI reconstruction model. We apply the Bregman iteration technique to handle the proposed optimization problem. During the
 iteration, the p-shrinkage operator is employed to resolve the nonconvex problem caused by the lp-norm. Experimental results illustrate that our algorithms could offer the higher SNR and lower relative error compared with traditional TV algorithms and high-degree
 TV (HDTV) algorithm in MRI reconstruction problem.