Plenary Lecture
A Wavelet based Approach for Image Reconstruction from Gradient Data and its Applications
Professor Pan Agathoklis
Department of Electrical and Computer Engineering
University of Victoria
Victoria, BC, CANADA
E-mail: panagath@ece.uvic.ca
Abstract: There are many applications where a 2-D function has to be obtained by numerically integrating gradient data measurements. In signal and image processing, such applications include rendering high dynamic range images on conventional displays, editing and creating special effects, as well as possible future digital photography where the cmera is sensing changes in intensity instead of intensity as it is the case in most cameras today. A common approach to deal with this 2-D numerical integration problem is to formulate it as a solution of a 2D Poisson equation and obtain the optimal least-squares solution using any of the available Poisson solvers. An alternative is to convert the surface normals to equivalent 2-D gradient data and solve this problem by a Fourier transform based integration method. Another area of application is in adaptive optics telescopes where wave front sensors provide the gradient of the wave front and it is required to estimate it by essentially integrating the gradient data. Several fast methods have been developed to accomplish this, such as the Multigrid Conjugate Gradient and Fourier transform techniques similar to those used in computer vision. Recently, a new reconstruction method based on wavelets has been developed and applied to image reconstruction for adaptive optics. This method is based on obtaining a Haar wavelet decomposition of the image directly from the gradient data and then using the well known Haar synthesis algorithm to reconstruct the image. This technique further allows the use of an iterative Poisson Solver at each resolution to enhance the visual quality of the resulting image. This talk focuses on image reconstruction techniques from gradient data and discusses the various areas where these techniques can be applied.
Brief Biography of the Speaker:Pan Agathoklis received the Dipl. Ing. degree in electrical engineering and the Dr. sc. techn. degree from the Swiss Federal Institute of Technology, Zurich, Switzerland, in 1975 and 1980, respectively. From 1981 until 1983, he was with the University of Calgary as a Post-Doctoral Fellow and part-time Instructor. Since 1983, he has been with the Department of Electrical and Computer Engineering, University of Victoria, B.C., Canada, where he is currently a Professor. He has received a NSERC University Research Fellowship and Visiting Fellowships from the Swiss Federal Institute of Technology, from the Australian National University and the University of Perth, Australia. He was Associate Editor for the IEEE Transactions on Circuits and Systems in 1990-1993 and he is currently Associate Editor for Multidimensional Systems and Signal Processing, CSSP and Journal of Electrical and Computer Engineering He has been member of the Technical Program Committee of many international conferences and has served as the Technical Program Chair of the 1991 IEEE PACRIM Conference the 1998 IEEE Symposium on Advances in Digital Filtering and Signal Processing and the 2009 ISSPIT. His fields of interest are in control, digital signal processing and their applications. He worked in the stability of multidimensional systems and in the application of 2D and 3D filtering in radio astronomy for removing radio interference. His interest in adaptive optics and its application in the development of optical telescopes lead to new solutions to the problem of image reconstruction from gradient data. These results are also being applied to problems in image processing like Poisson Editing, image stitching etc.