An approach to estimate noise, Rician signal bias and true signal in magnitude signal data obtained with magnetic resonance imaging. The method uses multiple measurements at different scan parameter settings, also referred to as weightings, and an iterative algorithm to estimate noise, expected signal and associated Rician signal bias. Measurements at all measured weighting levels contribute to the ultimate estimation of the bias-free signal decay function. Therefore, of the so processed magnetic resonance image data, weighted signals can be computed at arbitrary weighting levels and with considerably better signal-to-noise ratio than the originally obtained data at corresponding weightings. Bias-free weighted image data at desired weighting levels, maps of the decay function fit parameters, or maps of a combination of such decay function parameters can be used for rapid and highly sensitive tissue characterization.