Using Prior Knowledge in SVD-Based Parameter Estimation for Magnetic Resonance Spectroscopy—The ATP Example

Abstract

We introduce the knowledge-based singular value decomposition (KNOB-SVD) method for exploiting prior knowledge in magnetic resonance (MR) spectroscopy based on the SVD of the data matrix. More specifically, we assume that the MR data are well modeled by the superposition of a given number of exponentially damped sinusoidal components and that the dampings alphakappa, frequencies omegakappa, and complex amplitudes rhokappa of some components satisfy the following relations: alphakappa = alpha (alpha = unknown), omegakappa = omega + (kappa- 1)delta (omega = unknown, delta = known), and rhokappa = Ckapparho (rho = unknown, ckappa = known real constants). The adenosine triphosphate (ATP) complex, which has one triple peak and two double peaks whose dampings, frequencies, and amplitudes may in some cases be known to satisfy the above type of relations, is used as a vehicle for describing our SVD-based method throughout the paper. By means of numerical examples, we show that our method provides more accurate parameter estimates than a commonly used general-purpose SVD-based method and a previously suggested prior knowledge-based SVD method.