Most of PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. In particular, they often introduce an unnecessary numerical dissipation on regions where the image content changes rapidly such as on edges and textures. This thesis studies the magnitude data/imagery of magnetic resonance imaging (MRI) which follows Rician distribution. It analyzes statistically that the noise in the magnitude MRI data is approximately Gaussian of mean zero and of the same variance as in the frequency-domain measurements. Based on the analysis, we introduce a novel partial differential equation (PDE)-based denoising model which can restore fine structures satisfactorily and simultaneously sharpen edges as needed. For an efficient simulation we adopt an incomplete Crank-Nicolson (CN) time-stepping procedure along with the alternating direction implicit (ADI) method. The algorithm is analyzed for stability. It has been numerically verified that the new model can reduce the noise satisfactorily, outperforming the conventional PDE-based restoration models in 3-4 alternating direction iterations, with the residual (the difference between the original image and the restored image) being nearly edgeree. It has also been verified that the model can perform edge-enhancement effectively during the denoising of the magnitude MRI imagery. Numerical examples are provided to support the claim.

Approved for public release; distribution is unlimited / The radio channel places fundamental limitations on the performance of mobile ad hoc wireless networks. In the mobile radio environment, fading due to multipath delay spread impairs received signals. The purpose of this thesis is to develop a radio channel model and examine the effect of various parameters on channel behavior that is representative of environments in which mobile ad hoc wireless networks operate. The various physical phenomena considered are outdoor environments, fading and multipath propagation, type of terrains, and mobility (Doppler shift). A channel model based on a Tapped Delay Line (TDL) structure was developed and implemented in the MATLAB programming language, and the performance of the time-varying channel was studied by plotting the signal constellations. The simulation results indicate that the number of taps required in the TDL is 8 or less and the carrier frequency did not influence the performance significantly. The Jakes Doppler spectrum should be used in urban environments with high mobility; the Gaussian Doppler spectrum is the choice for low mobility urban environments and for the hilly terrain under both low and high mobility. / Civilian, Singapore Ministry of Defense