### Löthgren, Pia

- Department of Forest Economics, Swedish University of Agricultural Sciences

Conference abstract, 2010
# Maximum likelihood estimation of the parameters of a modified Rice distribution

Löthgren, Pia

The Rice distribution arises in many applications within the field of Magnetic Resonance, for instance in Magnetic Resonance Spectroscopy, where complex-valued signals disturbed by additive white noise are recorded. Signal processing and analysis are usually conducted in frequency domain. In this field it is more common to consider the absolute value of the discrete Fourier transform of the signal. In this way one can more visually see the structure of the signal and its different components. Since both real and imaginary parts of the Fourier transformed signal can be seen as being normally distributed with means μ_R and μ_I respectively and variance σ^2 we obtain, after taking the absolute value of the signal, a Rice distribution with non-centrality parameter υ=√(μ_R^2+μ_I^2 ) and scale parameter σ^2. In the past Maximum likelihood estimation of the parameters υ and σ^2 has mostly been done by direct optimization of the log likelihood, and often not simultaneously. However, this gives little information about the original parameters, μ_R and μ_I, and hence we propose a modified three parameter version of the Rice distribution. Recently an EM-algorithm with a conditional maximization step, a so called ECM-algorithm, for performing Rician regression has been suggested, which we show can be successfully used on simultaneous estimations of the three parameters of the modified distribution. The asymptotic properties of the estimators are obtained. Applications to real Magnetic Resonance Spectroscopy data will also be presented

23rd Nordic Conference on Mathematical Statistics: NORDSTAT 2010

### Löthgren, Pia

- Department of Forest Economics, Swedish University of Agricultural Sciences

- Department of Forest Economics, Swedish University of Agricultural Sciences

Probability Theory and Statistics

https://res.slu.se/id/publ/31762