In this paper, two local activity-tuned filtering frameworks are proposed for noise removal and image smoothing, where the local activity measurement is given by the clipped and normalized local variance or standard deviation. The first framework is a modified anisotropic diffusion for noise removal of piece-wise smooth image. The second framework is a local activity-tuned Relative Total Variat...

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-...

The analysis of functional magnetic resonance imaging (fMRI) data involves multiple stages of data pre-processing before the activation can be statistically detected. Spatial smoothing is a very common pre-processing step in the analysis of functional brain imaging data. This study presents a broad perspective on the influence of spatial smoothing on fMRI group activation results. The data obta...