Stochastic Multiresolution Image Sketching for Inverse Imaging Problems

TL;DR

This paper introduces ImaSk, a stochastic multiresolution image sketching algorithm that accelerates inverse imaging problem solutions like CT reconstruction by using variable resolution images to reduce computation.

Contribution

It presents a novel stochastic optimization method using multiresolution image domain sketching, improving efficiency in high-dimensional inverse imaging problems.

Findings

ImaSk converges linearly for strongly convex regularization.

Using more multiresolution operators reduces computational time.

Numerical results demonstrate effectiveness in CT reconstruction.

Abstract

A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both image and data sizes are large and therefore the forward model is costly to evaluate. Since several years algorithms from stochastic optimization are used for tomographic image reconstruction with great success by subsampling the data. Here we propose a novel way how stochastic optimization can be used to speed up image reconstruction by means of image domain sketching such that at each iteration an image of different resolution is being used. Hence, we coin this algorithm ImaSk. By considering an associated saddle-point problem, we can formulate ImaSk as a gradient-based algorithm where the gradient is approximated in the same spirit as the stochastic average gradient am\'elior\'e (SAGA) and uses at each iteration one of these multiresolution operators at random. We prove that ImaSk is linearly converging for linear forward models with strongly convex regularization functions. Numerical simulations on CT show that ImaSk is effective and increasing the number of multiresolution operators reduces the computational time to reach the modeled solution.