Thesis (M.Sc.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 81-84.

This thesis presents a new preconditioner for elliptic PDE problems on unstructured meshes. Using ideas from second generation wavelets, a multi-resolution basis is constructed to effectively compress the inverse of the matrix, resolving the sparsity vs. quality problem of standard approximate inverses. This finally allows the approximate inverse approach to scale well, giving fast convergence for Krylov subspace accelerators on a wide variety of large unstructured problems. Implementation details are discussed, including ordering and construction of factored approximate inverses, discretization and basis construction in one and two dimensions, and possibilities for parallelism. The numerical experiments in one and two dimensions confirm the capabilities of the scheme. Along the way I highlight many new avenues for research, including the connections to multigrid and other multi-resolution schemes.

A method is presented that allows the use of multiresolution principles in a time domain electromagnetic modeling technique that is applicable to general structures. Specifically, methods are presented that are compatible with the multiresolution time-domain (MRTD) technique using Haar basis functions that allow the modeling of general structures without limiting the cell size to the features of the modeled structure. Existing Haar techniques require that cells be homogenous in regard to PECs and other localized effects (with the exception that permeability and permittivity can vary throughout the cell). The techniques that are presented here allow the modeling of these structures using a subcell technique that permits the modeling of these effects at individual equivalent grid points. This is accomplished by transforming the application of the effects at individual points in the grid into the wavelet domain. There are several other contributions that are provided in this work. First, the MRTD technique is derived for a general wavelet basis using a relatively compact vector notation that both makes the technique easier to understand and allows the differences and similarities between different MRTD schemes more apparent. Second, techniques such as the uniaxial perfectly matched layer (UPML) for arbitrary wavelet resolution and non-uniform gridding are presented for the first time. Using these techniques, any structure that can be simulated in Yee-FDTD can be modeled with Haar-MRTD. For the first time, results for the use of a time-and-space-adaptive grid in an MRTD simulation are presented.

A system for extracellular neural interfacing that had the capability for stimulation and recording at multiple electrodes was presented. As the core of this system was a custom integrated circuit (IC) that contained low-noise amplifiers, stimulation buffers, and artifact-elimination circuitry. The artifact-elimination circuitry was necessary to prevent the activity of the stimulation buffers from interfering with the normal functioning of the low-noise amplifiers. The integrated circuits were fabricated in in a 0.35 micron CMOS process. We measured input-referred noise levels for the amplifiers as low as 3.50 microvolts (rms) in the in the bandwidth 30 Hz-3 kHz, corresponding to the frequency range of neural action potentials. The power consumption was 120 microwatts, corresponding to a noise-efficiency factor of 14.5. It was possible to resume recording signals within 2 ms of a stimulation, using the same electrode for both stimulation and recording. A filtering algorithm to remove the post-discharge artifact was also presented. The filtering was implemented using a field-programmable gate array (FPGA). The filtering algorithm itself consisted of blanking for the duration of the stimulation and artifact-elimination, followed by a wavelet de-noising. The wavelet de-noising split the signal into frequency ranges, discarded those ranges that did not correspond to neural signals, applied a threshold to the retained signals, and recombined the different frequency ranges into a single signal. The combination of the filtering with the artifact-elimination IC resulted in the capability for artifact-free recordings.

The topic of stereo video is getting more attention among these days due to its high quality of visual effect. However, the large volume of data is the problem of its application. The topic of this thesis is to investigate a compression technique by Wavelet compression on the stereo video data. There is much similarity between the parallax videos. This similarity is obtained by a motion compensation technique: the optical flow computing. Optical flow proposed by Horn and Schunck was originally developed in the field of computer vision for the application of moving detection. In this thesis we apply the optical flow to compress the similarity information between the parallax stereo video. On the other hand, the Wavelet transformation has been proved to be a successful technique for multiscale modeling. We therefore applying the Wavelet transform combined with the zerotree compression to compress the fields of optical flow. Experimental results in this thesis have demonstrated different effects in different situations.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 164-170).

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 110-115). Also available on the Internet.

Thesis (Ph.D.) -- University of Texas at Arlington, 2008.

Thesis (Ph. D.)--University of Queensland, 2001. / Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xxv, 142 p.; also includes graphics. Includes abstract and vita. Advisor: Yuan F. Zheng, Dept. of Electrical and Computer Engineering. Includes bibliographical references (p. 135-142).