An Efficient Interpolation Approach for Exploring the Parameter Space of Regularized Tomography Algorithms

Abstract

Choosing a regularization parameter for tomographic reconstruction algorithms is often a cumbersome task of trial-and-error. Although several automatic and objective criteria have been proposed, each of them yields a different “optimal” value, which may or may not correspond to the actual implicit image quality metrics one would like to optimize for. Exploration of the space of regularization parameters is computationally expensive, as it requires many reconstructions to be computed.

In this paper we propose an algorithmic approach for computationally efficient exploration of the regularization parameter space, based on a pixel-wise interpolation scheme. Once a relatively small number of reconstructions have been computed for a sparse sampling of the parameters, an approximation of the reconstructed image for other parameter values can be computed instantly, thereby allowing both manual and automated selection of the most preferable parameters based on a variety of image quality metrics.

We demonstrate that for three common variational reconstruction methods, our approach results in accurate approximations of the reconstructed image and that it can be used in combination with existing approaches for choosing optimal regularization parameters.