OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

 "Exploiting spatial context in the quantification of vector valued magnetic resonance data: a high-dimensional optimization problem "
   B. Michael Kelm, Björn H. Menze, Fred A. Hamprecht (University of Heidelberg)

Conventional imagery is increasingly complemented by spatially resolved vectorial or tensorial measurements that can help elucidate phenomena that would otherwise elude an unequivocal interpretation. While such data (e.g. spectroscopic images, image sequences, diffusion tensor images) potentially offer valuable additional information, they also pose difficult problems in signal processing, pattern recognition and optimization.

More specifically, and restricting this discussion to medical in vivo magnetic resonance (MR) studies, conventional MR images offer morphological information only. In recent years, new flavors of MR imagery have emerged, such as functional MR imaging for the study of brain activity, diffusion tensor imaging for the elucidation of tissue microstructure and brain connectivity, diffusion contrast enhanced (DCE) imaging for the derivation of pharmacokinetic parameters, or MR spectroscopic images (MRSI) for tumor detection and localization.

Our talk will focus on noisy DCE and MRSI images, and discuss strategies to incorporate spatial context in their analysis. In both cases, a parametric model is fit to the raw data. A spatial smoothness assumption is embodied in the potentials of a Markov Random Field, and the maximum a posteriori estimate is approximated by means of a block-iterated conditional modes algorithm. This heuristic for solving a high-dimensional optimization problem is shown to converge faster than conventional iterated conditional modes (ICM) and to produce parameter estimates with significantly smaller variance, leading to an overall reduction in mean squared error.