CS-MRA reconstruction based on nonsubsampled contourlet transform in frequency domain (NSCT-FD)

Abstract

Compressed sensing (CS) is a novel developed theoretical framework for information acquisition and processing. Taking advantages of the sparsity or compressibility inherent in real world signals, CS can collect compressed data at the sampling rate much lower than that needed in Shannon's theorem. When it has been used for medical imaging techniques, CS theory can fast the scanning speed of MRI, reduce the radiation doses and alleviate the patients' suffering. In order to obtain the effective sparse representation, the nonsubsampled contourlet transform in the frequency domain (NSCT-FD) is adopted, then an improved fast iterative soft thresholding algorithm (FISTA) is applied for CS-MRA reconstruction. This novel method not only inherits the simplicity and effectiveness of the original FISTA, and the sparse curvy representation ability of the contourlet transform, but also has the advantages of the shift-invariant property and much less computational burden. The performance is evaluated qualitatively and quantitatively both in noiseless and noisy situations, compared to the classic wavelet and the sharp frequency localization contourlet transform (SFLCT) method. Three quantitative indices are employed including the peak signal to noise ratio (PSNR), mutual information (MI) and relative l 2 norm error (RLNE) and qualitative performance evaluations use the profiles in horizontal direction and local region magnification comparison. Experimental results demonstrate the superiority of the NSCT-FD algorithm, displaying higher PSNR and MI, and lower RLNE indices in both noiseless and noisy MRA images, which have good reconstruction accuracy with reasonable real time computation speed. It is manifest that the NSCT-FD algorithm can be applied in fast medical imaging fields to achieve quality images in a relatively fast process, which will benefit cardiac and carotid MRI, dynamic MRI and MRA.