Statistics of MR Signals - Revisited

摘要

A common view in MRI research is that the object variability of MR signals is negligible. With this recognition, the signal components of MR signals are treated as constant and the noise components are studied as random processes. Because signal components of MR signals represent a collective behavior of a huge mount of spins, a statistical investigation may provide a better understanding of MR signals. The work reported in this paper first investigates statistics of the thermal equilibrium macroscopic magnetization (TEMM) which is the quantity to be imaged - one that can be measured and actually observed in MRI. Then it investigates statistics of the transverse precessing macroscopic magnetization (TPMM) which introduce an electromagnetic force in the receiver coil of MRI. Finally this study investigates statistics of signal components of three MR signals at the different stages of MR signal detection module: Free Induction Decay (FID), Phase Sensitive Detection (PSD), and Analog-to-Digital Conversion (ADC), sequentially, k-space sample is a reformatted ADC signal. The study derives and proves stochastic models for TEMM, TPMM, FID, PSD, and ADC signals, also proposes and justifies stochastic models for homogeneous and inhomogeneous samples. The study shows that under the normal conditions and the ordinary settings, magnetizations can be characterized as spatially deterministic processes with Probability one, and MR signals - signal component plus noise component - can be characterized as temporal Gaussian random processes with the means of signal components and the variances of noise components. These means are expressed in closed forms in terms of parameters of MR imaging system and the samples. The derived statistical properties of MR signals will serve as the basis for evaluating performances of imaging system and studying statistics of the MR image.