Efficient primal-dual algorithm for imaging applications with matrix stacking, applied to DBT image reconstruction

TL;DR

This paper improves the primal-dual hybrid gradient algorithm for tomographic imaging, simplifying parameter selection and demonstrating advantages in digital breast tomosynthesis image reconstruction.

Contribution

It introduces a simplified step-size selection method for the PDHG algorithm applicable to multi-term convex problems with linear transforms.

Findings

Enhanced quantitative accuracy in reconstructed volumes.

Improved depth resolution in DBT imaging.

Avoids extensive grid searches for optimal parameters.

Abstract

The primal-dual hybrid gradient (PDHG) algorithm for solving convex optimization problems that arise in tomographic imaging is revisited. In particular, simplification of the selection of step-size parameters is developed for optimization problems with multiple terms, each containing a linear transform subject to splitting. This simplification maintains algorithm efficiency while avoiding massive grid searches for the optimal parameter settings. The PDHG framework is demonstrated on an image reconstruction problem for wide-angle digital breast tomosythesis (DBT); use of the proposed optimization problem is enabled by the framework and it is demonstrated to have some advantage in quantitative accuracy of the reconstructed volume and in improving DBT depth resolution.