Detecting sparse signals and sparse connectivity in scale-space, with applications to the 'bubbles' task in an fMRI experiment
We are interested in the general problem of detecting sparse signals in an image, or more generally, sparse connectivity, or high correlation, between pairs of pixels or voxels in two sets of images. We extend this to searching over filter width or 'bubble' width, a so-called scale-space analysis. To do this, we set a threshold on the correlations that controls the false positive rate, which we approximate by the expected Euler characteristic of the excursion set. We apply this to an fMRI experiment using the 'bubbles' task. In this experiment, the subject is asked to discriminate between images that are revealed only through a random set of small windows or 'bubbles'. We are interested in which parts of the image are used in successful discrimination, and which parts of the brain are involved in this task.