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In the last half decade, fast methods of magnetic resonance imaging have led to the possibility, for the first time, of noninvasive dynamic brain imaging. This has led to an explosion of work in the Neurosciences. From a signal processing viewpoint the problems are those of nonlinear spatio-temporal system identification. Here, the authors develop new methods of identification using novel spatial regularization. They also develop a new model comparison technique and use that to compare their method with existing techniques on some experimental data.