Simultaneous identification of noise and estimation of noise standard deviation in MRI

INTRODUCTION Data analysis in MRI is sophisticated and can be thought of as a “pipeline” of closely connected processing and modeling steps. Because noise in MRI data affects all subsequent steps in this pipeline, e.g., from noise reduction and image registration to parametric tensor estimation [1] and uncertainty assessment [2], accurate noise assessment has an important role in MRI studies. Noise assessment in MRI usually means the estimation of noise variance (or standard deviation (SD)) alone [3-8]. Here, we will demonstrate that (I) the identification of noise, which has not received much attention in MRI literature, is as important as—if not more important than—the estimation of noise standard deviation (SD), (II) the identification of noise and the estimation of noise SD can be combined into a single coherent framework of noise assessment, and (III) this framework can be made self-consistent, that is, it can be turned into a fixed point (iterative) procedure. To this end, we propose a novel approach to simultaneously identify noise and estimate the noise standard deviation from a commonly used data structure (see Fig. 1) in MRI. i j k m(i,j,k) or mi,j,k or m[i][j][k]