Images from functional imaging experiments are subject to a data processing stream involving motion correction and spatial normalization. The next step is then to smooth the images using a Gaussian kernel. One reason for the smoothing step is to render activation information amenable to classical statistical inference via Random Field Theory. This requires that the residual fields have a smooth...

A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multiple taper estimate. This procedure reduces the expected mean square error by (π 2 4) 4/5 over simply smoothing the log tapered periodogram. A data adaptive implementation of a variable bandwidth kernel smoother is given.

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...