A hybrid MRI method based on denoised compressive sampling and detection of dominant coefficients

Abstract

In this paper, a hybrid method for acquisition and reconstruction of sparse magnetic resonance images is presented. The method uses conventional spin echo Magnetic Resonance Imaging (MRI) with only a few Phase-encoding steps to obtain the dominant k-space data coefficients. The rest of the k-space data coefficients are estimated using Compressive Sampling (CS). The compressive sampling part of the algorithm uses a random matrix to sample the vectorized k-space data of the image at a sub-Nyquist rate followed by reconstruction of the Discrete Wavelet Transform (DWT) coefficients of the k-space data using Orthogonal Matching Pursuit (OMP). The DWT coefficients are then transformed into the Discrete Fourier Transform (DFT) domain and denoised prior to combination with the dominant DFT coefficients obtained using conventional MRI to yield the whole k-space of the reconstructed image. The reconstructed k-space data is finally transformed into the reconstructed image using inverse DFT. Computer simulation results show that the proposed procedure yields better results than other conventional CS-MRI methods in terms of Peak Signal to Noise Ratio (PSNR) and Structural SIMilarity (SSIM) index.