Maximum Likelihood Estimation of the Distributional Parameters of the Magnitude and Phase in Magnetic Resonance Spectroscopy Signals

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Pia Lothgren*+
• Companies: Swedish University of Agricultural Sciences
• Keywords: Maximum likelihood estimation ; magnitude and phase signals ; magnetic resonance spectroscopy ; Rice distribution

Abstract

In magnetic resonance spectroscopy complex valued signals are disturbed by additive white noise. Signal processing are usually done in frequency domain, but in order to more visually see the structure of the signal within this field is it more common to consider the magnitude of the discrete Fourier transform of the signal. The complex Fourier transformed signal follows a bivariate normal distribution with parameters obtained from the unobserved signal magnitude and phase. Taking the absolute value yields the joint distribution for the magnitude signal and phase, for which the marginal distribution of the signal magnitude is known as the Rice distribution. Maximum likelihood estimation is done for the marginal distributions of magnitude and phase, respectively, and for the joint distribution for the two variables. The two approaches are compared and their asymptotic properties are derived.