<title>Regularization of the image division approach to blind deconvolution</title>

Abstract

In the unlikely event that the author did 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 indicrte the deletion. COMMITTEE ON OPTICAL SCIENCES (GRADUATE)In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHYIn the Graduate College THE UNIVERSITY OF ARIZONA STATEMENT BY AUTHORThis dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona £md 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 jjermission, provided that accurate 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 scholeirship. In all other instances, however, permission must be obtained from the author. SIGNED: ACKNOWLEDGMENTSFirst I have to thank my family for giving me the necessary strength to complete this rough journey.I owe a great debt to my advisor Dr. B. Roy Rrieden. Thanks to his guidance and patience I could finish this work.I especially must thank Dr. Shoemacker and the OSC staff, in particular Didi Lawson, who always help me without hesitation.I also want to thank Candido Pinto. He was the one who helped me to overcome most of the computer related problems that I confronted during this work.This research would not have been possible without the support of CONACYT (Mexico), and the University of Sonora (Mexico). DEDICATIONTo the memory of my mother.To my father. for 14 pixels support, (c) for 12 pixels supp., (d) for 10 pixels supp., (e) for 8 pixels supp., (f) for 6 pixels supp., (g) for 4 pixels supp., (h) for 2 pixels supp 45 FIGURE 3.5. Flow chart for the image division program 48 It is found that the system of linear equations, resulting from the implementation of the image division method, has a multiplicity of solutions. Moreover such sj'stem of equations is poorly conditioned. This brings the necessity of a regularization approach.This dissertation describes the development and implementation of a regulariza tion algorithm for the image division method. Using this regularization algorithm the blind deconvolution problem is posed eis a constrained lezist-squares problem. A least-squares solution is fovmd by computing a QR factorization of the system matrix.The Householder transformation method is used to find this factorization. The QR decomposition transforms the problem into an upper-triangular system of equations which is solved by bcicksubstitution. Prior pzirtial knowledge about the point-spread fimctions and the object (such as finite support and positivity) is used to impose constrziins on the solution, solving the multiplicity-solutions problem. 15The...