Sparse and Incomplete Signal Dictionaries for Reconstruction of MR Images

Abstract

Compressed Sensing(CS) is a mathematical approach for data acquisition in which the signals are compressible and sparse w.r.t. to an orthonormal basis. These sparse signals are reconstructed from very less measurements. CS technique Is widely used in Magnetic Resonance Imaging (MRI) where the doctors suggest the patients to undergo MRI scans for diagnosing their body parts. During the prolonged MRI Scan, the exact slice of the MRI cannot be achieved due to the difficulties faced by the patient or irregular changes in the body position of the patient. The idea is to reduce the exposure time of the patient’s body against the MRI scan by considering only fewer samples. Is it possible to Reconstruct the signal by making use of a fewer number of samples that are less than the Nyquist rate? Yes, it is possible to reconstruct the signal by making use of the Compressed Sensing or sampling Technique. Compressed sensing is a new framework for signal acquisition and representation in a compressible manner less below the Nyquist sampling rate. In this article, Sampling and reconstruction are dealt here thoroughly as part of the research activity. Compressive Sensing Matching pursuit (CoSaMP) is a novel technique for optimization. It is an iterative approximation method for sparse and incomplete signal recovery. CoSaMP method along with Different transform techniques is used for reconstruction. The FFT_CoSaMP, DCT_CoSaMP and DWT_CoSaMP are proposed methods for MR Image Reconstruction, where DWT-based CoSaMP along with different wavelet families give the best results when compared to other CS-based techniques w.r.t. PSNR, SSIM and RMSE analysis.