Undersampling k-space data is an efficient way to speed up the magnetic resonance imaging (MRI) process. As a newly developed mathematical framework of signal sampling and recovery, compressed sensing (CS) allows signal acquisition using fewer samples than what is specified by Nyquist-Shannon sampling theorem whenever the signal is sparse. As a result, CS has great potential in reducing data acquisition time in MRI. In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a basis, usually wavelet transform or total variation. In this paper, we propose an improved compressed sensing-based reconstruction method using the complex double-density dual-tree discrete wavelet transform. Our experiments demonstrate that this method can reduce aliasing artifacts and achieve higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index. 1. Introduction Magnetic resonance imaging (MRI) is one of the major imaging modalities in use today. Compared to computed tomography (CT), MRI has advantages in imaging soft tissues. However, its relatively long imaging time remains a great challenge for clinical application, often limiting its application. Significant efforts have focused on faster data collection as well as reducing the amount of data required without degrading image quality. For example, parallel imaging [1–3] exploits redundancy in k-space by introducing multiple receiver channels, mitigating the aliasing artifacts caused by a reduced sampling rate. Recently, compressed sensing based MRI (CS-MRI) allows high quality reconstruction from undersampled data by enforcing the pseudo-sparsity of images in a predefined basis or dictionary, such as the traditional two-dimensional (2D) separable wavelet transform or total variation [4]. However, these basis sets may not provide sufficient sparse representation. The discrete wavelet transform (DWT), for example, has three major disadvantages: shift sensitivity [5], poor directionality [6], and lack of phase information [7, 8]. For these reasons, traditional DWTs fail to capture regularities of contours, since they are not able to sparsely represent one-dimensional singularities of 2D signals [9]. Therefore, improvements can be obtained by mitigating some of these disadvantages simultaneously. In this paper, we propose an improved compressed sensing method for MR imaging by utilizing the double-density dual-tree DWT [10]. The use of complex wavelet transforms for compressed sensing was first proposed in [11]. The authors in [11] used
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