Accelerated Exponential Fitting for Rapid Relaxation Time Mapping

Introduction Mapping of relaxation times such as T1 and T2 generally involves the fitting of an exponential function to the evolution of the signal intensity in each pixel of a time series of images. The prevalent method employed for this purpose, the Levenberg-Marquardt method, pursues a non-linear least squares approach [1]. For applications that require a rapid mapping, its high computational complexity is a limiting factor, however. Other, faster methods have been devised, but they prove less accurate. For instance, a linear regression leads to an unstable estimation in the presence of noise, and a numerical integration to a systematic overestimation [2]. To decrease computational complexity while conserving accuracy, the present work suggests to solve the non-linear regression problem by searching for a real root of a polynomial in a small interval, and it demonstrates this approach on T2 * mapping. Methods Let sk denote the samples of signal intensity taken at k∆t, where k = 0 ... N-1. The best fit of a monoexponential decay to this time series in a least squares sense is given by the minimum of the error function