A least square estimator for spin-spin relaxation time in magnetic resonance imaging

Magnetic Resonance (MR) imaging techniques are widely used for medical examination of biophysical properties of tissues. Clinical diagnoses are mainly based on the evaluation of contrast in MR images, evaluating the water component of involved tissues. Moreover, weighted images are considered in order to evaluate the difference response time in order to detect pathologies such as cancer. In this paper we propose some some first results of a statistical technique able to estimate the Spin-spin Relaxation Time of observed tissues exploiting both real and imaginary parts of MR images. Working in the complex domain instead of the amplitude one allows us to write the joint probability distribution of real and imaginary signals. Considering the optimal estimator for the considered case, we are able to evaluate the tissues relaxation times with the lowest possible variance. This estimation technique can lead to a different scenarioes in medical diagnostic. The method has been tested on real data, showing interesting results