Bayesian random projection-based signal detection for Gaussian scale space random fields

In the present paper, we are concerned with introducing a simple method for signal detection problem in one realization of a two-dimensional random field based on the one-dimensional random projection technique. Formally, we provide a Bayesian projection-based approach for signal detection in the two-dimensional Gaussian scale space random field, though it is applicable for higher dimensions. It will be shown by a series of simulation studies that our purposed method, controls the error rate in nominal level and has the high performance for signal detection, and this procedure completely distinguishes between the two hypotheses of "no signal" and the alternative. Also, we provide two applications of the proposed procedure, one from a real dataset of a two-dimensional random field of R-fMRI data of an autistic individual and the other with a two-dimensional random field of fMRI data.