Compressive Sensing Magnetic Resonance Imaging (CS-MRI) has been rapidly developed during last several years.
To reconstruct an image from incomplete data using compressive sensing, the image has to be sparse or can be
transformed to sparse representation. Gradient operators associated with total variation (TV) and discrete wavelet
transform (DWT) are two commonly used sparsifying transforms in CS-MRI. Since the data acquired in MRI are
complex, these transforms are usually applied to the real and the imaginary parts of the image independently. In this
paper, we will explore the application of the complex wavelet transform (CWT) as a more effective sparsifying
transform for CS-MRI. Specifically, dual-tree complex wavelet transform (DT-CWT), a CWT previously used for
real or complex image compression, is integrated with compressive sensing reconstruction algorithm. We will test
the new method using both simulated and in-vivo MRI data. The results will be compared with those of DWT and
TV, which show that the new method can achieve better sparsity and reduced reconstruction errors in CS-MRI.