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摘要
Magnetic resonance imaging (MRI) has been widely employed in medical diagnosis, since it enables superior visualization of anatomical structure with noninvasive and nonionizing radiation nature. However, during the data acquisition process of MRI, patients' translational motion usually leads to phase changes of the observed data; moreover, the amplitudes of the observed data are usually contaminated by noises. In this paper, we assume that the phase and amplitude noises, respectively, cause the phase and amplitude changes of the observed data. Therefore, how to reconstruct high-quality magnetic resonance (MR) images via highly undersampled K-space data with noises is a challenge. To address this issue, a novel MR image reconstruction model, named the adaptive tight frame and total variation MR image reconstruction model (TFTV-MRI), is proposed based on the compressed sensing (CS) theory. TFTV-MRI fuses the adaptive tight frame (ATF) learning and total variation (TV) into the image reconstruction model. The sparse representations of MR images in tight frame domain can adapt to the MR image by itself, simultaneously, the advantage of TV is better edge preserving property and MR images are sparse in gradient domain. Differing from the l(0)-norm or l(1)-norm utilized in traditional AFT learning, we exploit the logarithm penalty term to measure the sparsity of MR images in TFTV-MRI. The alternating iterative minimization algorithm is utilized to tackle the optimization problem of TFTV-MRI, including ATF learning step and MR image reconstruction step. In MR image reconstruction step, the inertial proximal algorithm for nonconvex optimization is employed. The experiments verified that the proposed model achieved the superior performance for dislodging the phase noises caused by the translational motion and removing the amplitude noises of the observed data, and reconstructed MR images nicely in different sampling schemes. Compared with the existing methods, the proposed approach can achieve higher accurate image reconstruction quality, faster convergence speed, and better robustness to noises.
