Reference-less MR Thermometry Using Iteratively-Reweighted L1 Regression

Introduction Proton resonance frequency(PRF-) shift MR thermometry is a promising tool for monitoring thermal therapies. In PRF-shift thermometry, maps of relative temperature changes are estimated by subtracting image phase in a pretreatment (baseline) state from image phase in a heated state. Baseline phase can be obtained from a pretreatment image, however, this approach is sensitive to motion and reduces SNR by 2 . Reference-less thermometry methods [1,2] avoid these issues by estimating temperature from a single image via least-squares (L2) polynomial regression and extrapolation. To avoid temperature misestimation, current reference-less methods require that the hot spot be masked out of the polynomial regression. This complicates their application, since the user must either know a priori the location of the hot spot, or employ a sophisticated tracking algorithm to follow it [3]. We propose a new reference-less thermometry method that uses robust regression so that the hot spot need not be masked out. The method therefore requires no human interaction or tracking to obtain accurate temperature maps, and is inherently robust to motion. Theory Reference-less thermometry methods assume that in the absence of therapy-induced temperature changes, image phase varies smoothly over space and can be accurately represented as a superposition of low-order polynomial basis functions, the coefficients of which are estimated via regression. In this context, the phases at spatial locations within the hot spot are regarded as outliers whose influence on the estimates is to be avoided. L1 regression is a natural choice for this problem, since it is inherently robust to outliers. In our application, the L1-optimal polynomial coefficients are given by: