ABSTRACT
As shown in Chapter 3, MR images are reconstructed from k-space samples, while k-space samples are formulated from analog-to-digital conversion (ADC) signals by applying adequate pulse sequences. An ADC signal is a discrete version of a phase sensitive detection (PSD) signal (sampled at the proper frequency), while a PSD signal is formed from a free induction decay (FID) signal via quadrature PSD. FID signals are induced by transverse precessing macroscopic magnetization (TPMM), while TPMM originates from thermal equilibrium macroscopic magnetization (TEMM). Thus, in MR imaging, the term MR data means the macroscopic magnetiza-
tions (TEMM, TPMM), MR signals (FID, PSD, ADC), and k-space samples. Among them, TEMM is spatially distributed, TPMM varies with both time and the spatial location, FID, PSD and ADC are the temporal signals, and k-space samples are in the spatial frequency domain. TEMM and FID are real data; TPMM, PSD, ADC, and k-space samples are complex data. Similar to any type of realistic data, each type of MR data consists of its signal and noise components. In some statistics studies on MR imaging, the randomness of the signal
components of MR data is ignored. Therefore, the randomness of MR data is mainly derived from their noise components, particularly from the thermal noise [1-3, 5-7, 9-11, 13, 14, 16, 17, 23, 27, 53-56]. MR noise studies are often associated with the signal-to-noise ratio (SNR) evaluation. This is because the SNR can provide an absolute scale for assessing imaging system performance and lead to instrumentation design goals and constraints for system optimization; also, it is one of the fundamental measures of image quality. This chapter describes statistics of both signal and noise components of each
type of MR data, and focuses on their second-order statistics. Based on the physical principles of MRI described in Chapter 3 and according to MR data acquisition procedures, the statistical description of MR imaging progresses in the following natural and logical order: macroscopic magnetizations (TEMM → TPMM) =⇒ MR signals (FID → PSD → ADC) =⇒ k-space samples. When MR data travel in the space-time-(temporal and spatial)–frequency domains, their statistics are evolving step by step.
