Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object

TL;DR

This paper addresses the challenge of reconstructing 3D objects in diffraction tomography when the object moves irregularly, proposing a TV-based phase retrieval method for practical intensity-only measurements.

Contribution

It introduces a TV-regularized phase retrieval algorithm for diffraction tomography with moving objects, applicable when only intensity data is available.

Findings

The proposed method effectively reconstructs objects from intensity-only measurements.

It handles irregular, time-dependent object rotations in diffraction imaging.

The approach outperforms traditional methods in scenarios with limited phase information.

Abstract

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an irregular, time-dependent rotation under acoustical or optical forces. In this study, we compare reconstruction algorithms in case i) that two-dimensional images of the complex-valued wave are known, or ii) that only the intensity (absolute value) of these images can be measured, which is the case in many practical setups. The latter phase-retrieval problem can be solved by an all-at-once approach based utilizing a hybrid input-output scheme with TV regularization.