Compressed sensing (CS) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of\ntranslation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in\nserious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree\ndiscrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce\nsuch visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity.\nIn addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based\nreconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio\n(PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error.
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