Date of Award

12-15-2006

Degree Type

Dissertation

Degree Name

Ph.D.

Degree Program

Engineering and Applied Science

Department

Physics

Major Professor

Ioup, George

Second Advisor

Ioup, Juliette

Third Advisor

Puri, Ashok

Fourth Advisor

Herrington, Paul

Fifth Advisor

Outlaw, Curtis

Sixth Advisor

Hou, Weilin

Abstract

This research consists of three parts. The first part is an investigation of several popular image restoration techniques. The techniques are used to restore 2-D image data, f(x, y), that has been blurred by a known point spread function (PSF), b(x, y) and corrupted by an unknown amount of noise, n(x, y). Several sample images are restored using all of the techniques. Of the methods investigated the one which produces the best restoration results was determined to be the Wiener deconvolution method. The determination of the best method is based on the quality of the restored image and the required restoration time. The second part of this research involves the development of a noise standard deviation ( n) estimation method. The method determines an estimate, e, of n based on the Morrison Noise Reduction Method (MNRM) and is therefore an iterative method. The results of the noise, n, estimating method (SIGEST) developed are rather good. The error between n and e when average across several images all contaminated with a medium width or greater PSF and various amounts of noise, is less than 10 percent. Knowledge of n is important for the application of Wiener deconvolution. All noise in this research is assumed to be uncorrelated noise. The third part of this research involves the development of the Sub-Imaging Method, SIM. In the third part of this research, the h2 and the hN of image data h is defined as follows: h2 = Image data h processed by two iterations of the MNRM hN = h – h2 SIM divides an image's hN into several rectangular parts, calculates e of each part by the method described previously, calculates the average of the e‘s and selects the part with a e which is closest to the average of all the e‘s. The part with a e closest to the average is defined to be the average sub-image (asi). The following assertions concerning SIM are investigated: 1. The asi of an image can be used in the place of the whole image to determine e of n and used to restore the whole image. Therefore, the noise in a piece of an image can represent the noise in the whole image (provided it is the asi of the image's hN). 2. SIM can be combined with the Wiener image restoration method to restore contaminated image data without the n of the data initially being known. In this research, image and numerical results are provided which validate the two claims about SIM. The wiener method and SIM are combined to develop the Sub-Image Wiener Method (SIWM). In this research, image and numerical results are provided to show that SIWM is an effective method of restoring blur and noise contaminated image data. Image and numerical data are provided comparing SIWM to the Matlab function Wiener2. The results show that SIWM is faster and yields better results than the Wiener2 method. .

Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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