Engineering Commons^™

A Spline Framework For Optimal Representation Of Semiperiodic Signals, Farzin G. Guilak

Dissertations and Theses

Semiperiodic signals possess an underlying periodicity, but their constituent spectral components include stochastic elements which make it impossible to analytically determine locations of the signal's critical points. Mathematically, a signal's critical points are those at which it is not differentiable or where its derivative is zero. In some domains they represent characteristic points, which are locations indicating important changes in the underlying process reflected by the signal.

For many applications in healthcare, knowledge of precise locations of these points provides key insight for analytic, diagnostic, and therapeutic purposes. For example, given an appropriate signal they might indicate the start or …

Image Super-Resolution Using Adaptive 2-D Gaussian Basis Function Interpolation, Terence D. Hunt

Theses and Dissertations

Digital image interpolation using Gaussian radial basis functions has been implemented by several investigators, and promising results have been obtained; however, determining the basis function variance has been problematic. Here, adaptive Gaussian basis functions fit the mean vector and covariance matrix of a non-radial Gaussian function to each pixel and its neighbors, which enables edges and other image characteristics to be more effectively represented. The interpolation is constrained to reproduce the original image mean gray level, and the mean basis function variance is determined using the expected image smoothness for the increased resolution. Test outputs from the resulting Adaptive Gaussian …