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