Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering

First Advisor

J. P. Basart


The main objective of this dissertation is to extract parameters from multiple wavelength images, on a pixel-to-pixel basis, when the images are corrupted with noise and a point spread function. The data used are from the field of radio astronomy. The very large array (VLA) at Socorro in New Mexico was used to observe planetary nebula NGC 7027 at three different wavelengths, 2 cm, 6 cm and 20 cm. A temperature model, describing the temperature variation in the nebula as a function of optical depth, is postulated. Mathematical expressions for the brightness distribution (flux density) of the nebula, at the three observed wavelengths, are obtained. Using these three equations and the three data values available, one from the observed flux density map at each wavelength, it is possible to solve for two temperature parameters and one optical depth parameter at each pixel location;Due to the fact that the number of unknowns equal the number of equations available, estimation theory cannot be used to smooth any noise present in the data values. It was found that a direct solution of the three highly nonlinear flux density equations is very sensitive to noise in the data. Results obtained from solving for the three unknown parameters directly, as discussed above, were not physical realizable. This was partly due to the effect of incomplete sampling at the time when the data were gathered and to noise in the system;The application of rigorous digital parameter estimation techniques result in estimated parameters that are also not physically realizable. The estimated values for the temperature parameters are for example either too high or negative, which is not physically possible. Simulation studies have shown that a "double smoothing" technique improves the results by a large margin. This technique consists of two parts: in the first part the original observed data are smoothed using a running window and in the second part a similar smoothing of the estimated parameters are done. This method provides an improvement over the previous method of directly solving the three nonlinear flux density equations when no adjacent pixel information was taken into account. When using the double smoothing technique, results were obtained that were not only physical realizable, but also compared well with previous results obtained from a two dimensional solution of the problem, assuming a constant temperature along the line of sight;To conclude the investigation, an approximate solution was found for the same temperature and optical depth parameters. This solution takes into account approximations that can be made as a result of the physical characteristics of the nebula as well as the results obtained from the previous 2-D study.



Digital Repository @ Iowa State University,

Copyright Owner

Willem C. Venter



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238 pages