Iterative improvement of lineshape estimation

Abstract

Magnetic Resonance Spectroscopy (MRS) is an effective diagnostic technique for monitoring metabolic and biochemical changes within an organism or sample. Static and dynamic inhomogeneity of the magnetic field applied to the patient distorts the function that governs the natural damping of the MRS signals. This damping function can be expressed in the frequency domain as a Lorentzian, Gaussian, or Voigt function; however, using these approximations, estimation of the desired in vivo metabolite concentrations may be biased.

We investigate by means of simulations whether estimation of the unknown distorted damping function can improve the overall result. Using an improved damping function decreases bias, but increases variance because more parameters are involved. It is, therefore, important to find a suitable bias-variance trade-off. Our method improves on that in Ref [1] by including iterations, consisting of applying Hankel Singular Value Decomposition (HSVD) and Nonlinear Least Squares (NLLS) to estimate a common damping function that is finally applied to a metabolite database [2]. For our simulations we use a signal with 11 undamped Lorentzian components inspired by the benchmark signal of ³¹P provided by [3]. Results show that by identifying the right model complexity using a convenient number of Lorentzians, the iterative method improves the parameter estimates significantly.