A Wavelet Based Approach for Image Reconstruction from Gradient Data and its Applications

摘要

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.