Synchronization of neural activity from distant parts of the brain is crucial for the coordination of cognitive activities. Because neural synchronization varies both in time and frequency, time–frequency (T-F) coherence is commonly employed to assess interdependences in electrophysiological recordings. T-F coherence entails smoothing the cross and power spectra to ensure statistical consistenc...

In this paper we develop elements of the global calculus of Fourier integral operators in Rn under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of s...

The purpose of this paper is to provide a general technique for defining and analyzing smoothing operators for use in multigrid algorithms. The smoothing operators considered are based on subspace decomposition and include point, line, and block versions of Jacobi and Gauss-Seidel iteration as well as generalizations. We shall show that these smoothers will be effective in multigrid algorithms ...

Analytic formulae are obtained for the smoothing factors yielded by Gauss-Seidel relaxation in two-color ordering for a class of scalar elliptic operators. Block and point relaxation, in conjunction with full or partial coarsening, are encompassed for operators with general (constant, positive) coeecients in general dimensions and for an arbitrary number of relaxation sweeps. It is found that t...

We propose a new class of non-linear image recovery operators based on local smoothing applied both in the spatial domain (horizontal smoothing) and in the gray-level domain (vertical smoothing). The commonly used horizontal smoothing gives the way of reducing the noise level (noise filtering), whereas the vertical smoothing yields the edge preservation property. The method is indexed by a real...

The aim of this study is to detect masses in mammograms through pipelining sequences of visualization operators. Such sequences act as morphological filtering operators for identifying objects of interest. This is done using series of rendering operators including edge detection, smoothing, filling small holes, coloring various densities, joining broken boundaries and eliminating small projecti...

The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are L2 bounded projections, and still they commute with the exterior derivative. In the present paper we general...

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and averaging. Recently double aggregation operators have been introduced; they model multistep aggregation process. The choice of aggregation operators depends on the particular problem, and can be done by fitting the operator to empirical data. We examine fitting general aggregation operators by usi...

We study a general class of nonlinear and shift-varying smoothing filters that operate based on averaging. This important class of filters includes many well-known examples such as the bilateral filter, nonlocal means, general adaptive moving average filters, and more. (Many linear filters such as linear minimum mean-squared error smoothing filters, Savitzky–Golay filters, smoothing splines, an...