Wavelet Domain Image Restoration and Super-Resolution

Abstract

In the unlikely event that the author dkl not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERINGIn Partial Fulfillment of the Reciuirements For the Degree of DOCTOR OF PHILOSOPHY STATEMENT BY AUTHORThis dissertation has been submitted in partial fulfillment of recjuirements for an advanced degree at The University of Arizona and is deposited in the University Library'' to be made available to borrowers under rules of the Library.Brief quotations from this dissertation are allowable without special permission, provided that acciurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. An especially deep note of appreciation is due to my wife Tamara for the love and encouragement she provided every step of the way during this program, and also for the past ten years that brought us to this point. Although she may not understand much past this point, she fills my life with joy in a way nothing else can.Finally I want to thank the Creator of all we see and that which I study, and his son, Jesus, who sustains me daily. "It is the glory of God to conceal a matter; to search out a matter is the glory of kings.' Proverbs 25:2 (NIV) It is glorious to ponder the way He has set things in motion and continues to sustain them! 5 LIST OF FIGURESFIGURE 2.1. Model of a general imaging system 18 FIGURE 2.2. 3-D plot of (a) jinc^, the PSF for a circular aperture imaging system and (b) the related MTF 21 FIGURE 2.3. 1-D plot of (a) jinc function, (b) jinc^ fimction, the PSF for a circular aperture imaging system, and (c) the related MTF. Note that the dotted line in (c) is the triangle function (straight line) for comparison. 22 The ability to super-resolve imagery using wavelet-domain techniciues is the second major focus of this research. Super-resolution, the ability to reconstruct object information lost in the imaging process, has been an active research area for many years. Multiple experiments are presented which demonstrate the possibilities and problems associated with super-resolution in the wavelet-domain. Finally, superresolution in the wavelet domain using Non-Linear Interpolative Vector Quantization is studied and the results of the algorithm are presented and discussed.14 CHAPTER 1