Undersampling ??-space data is an efficient way to speed up the magnetic resonance imaging (MRI) process. As a newly developed\r\nmathematical framework of signal sampling and recovery, compressed sensing (CS) allows signal acquisition using fewer samples\r\nthan what is specified by Nyquist-Shannon sampling theorem whenever the signal is sparse. As a result, CS has great potential in\r\nreducing data acquisition time in MRI. In traditional compressed sensing MRI methods, an image is reconstructed by enforcing\r\nits sparse representation with respect to a basis, usually wavelet transform or total variation. In this paper, we propose an improved\r\ncompressed sensing-based reconstruction method using the complex double-density dual-tree discrete wavelet transform. Our\r\nexperiments demonstrate that this method can reduce aliasing artifacts and achieve higher peak signal-to-noise ratio (PSNR) and\r\nstructural similarity (SSIM) index.
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