Stochastic Multiresolution Image Sketching for Inverse Imaging Problems
Journal:
arXiv
Published Date:
Dec 13, 2024
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.
