Fig. 3.

An estimate for the global posterior optimizer ${\mathbf{x}}_k$ obtained for the source space ${\mathcal{S}}_k$ is found using the estimate for ${\mathbf{x}}_{k-1}$ as the initial guess (“ Randomized Scanning” section). We consider this approach necessary in order to maintain the estimates as close to the global optimum as possible. Namely, using a fixed initial guess might mean that the global optimizer is not found for some of the source spaces. Left: The global posterior optimizer is found for the posterior of space 1 (solid contours). Right: For space 2 (dashed contours), it is found (solid grey path), if the final estimate obtained in the case one 1 is used as the initial guess for 2 (grey circled point), while a local optimizer is obtained (dashed grey path) with the original initial guess 1 (black circled point) resulting in an optimization error. The global optimum might, in practice, correspond to a situation in which both a superficial and deep source are detected, while the deep activity might be undetected at the local one