Coordinate transformations for approximate LSI modeling of LSV systems, and applications to restoration

摘要

A method is presented for finding coordinate transformations (warpings) of "objects" and "images," related by a shift-variant linear system model, such that the warped objects and images are approximately related by a shift-invariant linear system model. Such warps have utility for inverse solutions to linear problems, in which solution times for shift-invariant systems are less than the solution times for shift-variant systems. To this end, a measure of shift-variance for sampled linear systems is proposed. This measure allows for a variability in the sampling locations, as well as separable multipliers in the object and image domains (collectively called warping parameters), so that the measure may be used as the objective function for an optimization problem. Properties of the desired solution, which includes adequate field coverage and limits on the allowable warps, are also proposed. These features are combined in a formally stated optimization problem, which will search for a set of sample locations and multipliers to minimize the shift-variance of the warped system. The performance of a number of optimization algorithms which were directed at this task are presented. Also reported are results for finding the optimal warpings for some example one-dimensional systems. Inverse solutions, using both linear and non-linear techniques, are obtained using this warping method, and these results are compared to related inverse solutions which directly perform shift-variant inversion.