Single Image Signal-to-Noise Ratio Estimation for Magnetic Resonance Images

Signal-to-noise ratio (SNR) is a significant factor to quantify noise content, particularly in magnetic resonance imaging (MRI). MRI is used to generate high quality medical images in biomedicine and other research areas. In this thesis, two new approaches of SNR calculation for MRI system is developed and implemented for error minimization. The supreme proposed method applies the cubic spline interpolation with Savitzky-Golay (CSISG) technique in addition to using Gaussian mixture model decomposition (GMMD) algorithm to eliminate the energy of noise and increase the accuracy in SNR estimation. This approach is found to accomplish stunning results while compared with other existing methods as well as cross correlation function (CCF) and cubic spline interpolation with Savitzky-Golay (CSISG) approaches. Unlike other, the suggested approach is based on a single MR image, which generates consistency and accuracy in SNR estimation. A new noise reduction approach, based on cubic spline interpolation with Savitzky-Golay (CSISG) and GMMD, is developed. The GMMD-CSISG represented the tremendous outcome for SNR evaluation of MR imaging systems. Another technique has been designed to estimate the SNR for MR images. This technique exposed that cross-correlation of two acquisition of the same image could be applied in an extremely efficient approach for the MR system. We conduct several tests on various MRI according to the important characteristics of an MR image such as, phase relative to the RF transmitter phase, frequency, and magnitude. For approximation of perfect noise level shifting a general expression has been originated through a third degree polynomial curve fitting according to outcomes of these experimentations. The procedure uses single MR image to attain SNR value. The capability to define the SNR from a single MR image allows suggested method to be valid for online and offline image evaluation instantaneously. Keywords: Signal-to-Noise Ratio, Magnetic Resonance Imaging, Gaussian Mixture Model Decomposition, Auto-Correlation Function, Cross-Correlation Function.