A robust magnetic resonance imaging method based on compressive sampling and clustering of sparsifying coefficients

Abstract

This paper presents a novel and robust method for medical Magnetic Resonance Imaging (MRI). The proposed method utilizes the sparsity as well as clustering of the image coefficients in the wavelet transform sparsifying domain. The method shows better immunity to reconstruction noise than other Compressive Sampling (CS) based techniques. The algorithm starts with undersampling of the k-space data of the image using a random matrix followed by reconstruction of the Haar transform coefficients of the k-space data using the Orthogonal Matching Pursuit (OMP) algorithm. The transform coefficients are then modulated by a raised-cosine shaping vector that suppresses noisy artifacts in the coefficients to restore the clustering. The shaped coefficients are then transformed into k-space data. The k-space data is finally transformed into the image in spatial domain. Experimental results show that the proposed procedure gives better results than other conventional methods in terms of terms of Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE).