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Biometrika 1995 82(2):237-250; doi:10.1093/biomet/82.2.237
© 1995 by Biometrika Trust
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A Bayesian approach to synthetic magnetic resonance imaging

INGRID K. GLAD and GIOVANNI SEBASTIANI

Department of Mathematical Sciences, The Norwegian Institute of Technology 7034 Trondheim, Norway

Synthetic magnetic resonance imaging involves the estimation, based on a set of measured images with noise, of three basic physical quantities that are nonlinearly related to the observations. The methods currently available for this ill-conditoned inverse problem either do not provide sufficiently accurate estimates or require time-consuming data collection. We formulate this nonlinear problem in a Bayesian framework, taking into account knowledge about the physics of the magnetic resonance imaging experiment, statistical properties of the experimental noise, and prior information about the underlying physical quantities, modelled by a suitable Markov random field. A new multilayer Markov random field is proposed. Inference is drawn by means of Markov chain Monte Carlo methods or iterated conditional modes. Some examples are included to demonstrate how synthetic magnetic resonance imaging by this approach can be performed in an accurate and reliable way.

Key Words: Bayesian inference • Inverse problem • Iterated conditional modes • Magnetic resonance • Markov random field • Medical imaging • Markov chain Monte Carlo • Synthetic imaging • Tissue characterisation


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