Revisiting $\Psi$DONet: microlocally inspired filters for incomplete-data tomographic reconstructions

TL;DR

This paper enhances the $ ext{ extbackslash Psi}$DONet method for incomplete-data tomography by providing microlocal insights, refining its implementation with artifact-inspired filters, and demonstrating improved performance in sparse-angle scenarios.

Contribution

It offers a deeper microlocal interpretation of $ ext{ extbackslash Psi}$DONet, refines its implementation with specialized filters, and extends its application to sparse-angle tomography.

Findings

Reduced number of learnable parameters without loss of quality

Improved reconstruction quality from limited-angle data

Proof-of-concept for sparse-angle tomography

Abstract

In this paper, we revisit a supervised learning approach based on unrolling, known as $\Psi$DONet, by providing a deeper microlocal interpretation for its theoretical analysis, and extending its study to the case of sparse-angle tomography. Furthermore, we refine the implementation of the original $\Psi$DONet considering special filters whose structure is specifically inspired by the streak artifact singularities characterizing tomographic reconstructions from incomplete data. This allows to considerably lower the number of (learnable) parameters while preserving (or even slightly improving) the same quality for the reconstructions from limited-angle data and providing a proof-of-concept for the case of sparse-angle tomographic data.