James Nagy, Emory University
Keywords: Imaging
Abstract:
Many methods are available to restore an image from blurred and noisy data. In some cases simple filtering techniques, such as the Wiener filter, can be very effective. For more difficult problems, such as for spatially variant blurs or when enforcing physical constraints (e.g., non-negativity), iterative methods must be used. The cost of an iterative scheme depends on the amount of computation needed per iteration, as well as on the number of iterations needed to reach a good restoration of the image. Much work has been done to optimize cost per iteration, for both serial and parallel implementations. However, very little work has been done to develop robust schemes to accelerate convergence.
Preconditioning is a classical approach used in many areas of scientific computing to accelerate convergence of iterative methods. However, if not done carefully for image restoration (which is an ill-posed problem), preconditioning can lead to erratic convergence behavior that results in fast convergence to a poor approximate solution. In this paper we show how to overcome these difficulties. Specifically, we describe a robust preconditioning scheme for image restoration problems, where the preconditioner is constructed from the PSF and noise properties. To avoid erratic convergence behavior, regularization is naturally incorporated into the construction of the preconditioner. We show that with proper implementation, the overhead of using preconditioning for typical iterative methods, such as conjugate gradients, is about 1.5 times that of using no preconditioning, but that number of iterations can be reduced dramatically, resulting in a substantial reduction in overall cost of the iterative scheme. We show that our preconditioning scheme can be applied to spatially invariant and spatially variant blurs, to multi-frame deconvolution problems, as well as to algorithms that enforce non-negativity constraints. Several examples will be given to illustrate the performance of our preconditioning scheme.
Date of Conference: September 12-15, 2007
Track: Imaging