Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data

TL;DR

This paper introduces a novel iterative algorithm for joint estimation of scatter and attenuation images from broken ray transform data, improving reconstruction quality in tomographic imaging with noisy measurements.

Contribution

It presents the first joint estimation algorithm based on Poisson models for single-scatter data, with guaranteed monotonic likelihood reduction and a fast BRT forward operator computation.

Findings

Joint estimation outperforms single-image methods in certain scenarios.

Transmission data helps resolve low-frequency ambiguities.

Multiple scatter measurements improve attenuation image quality.

Abstract

The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events and nonlocal attenuation. Prior works focus on reconstructing one of two images: scatter density or total attenuation. However, both images are media specific and useful for object identification. Nonlocal effects of the attenuation image on the data are summarized by the broken ray transform (BRT). While analytic inversion formulas exist, poor conditioning of the inverse problem is only exacerbated by noisy measurements and sampling errors. This has motivated interest in the related star transforms incorporating BRT measurements from multiple source-detector pairs. However, all analytic methods operate on the log of the data. For media comprising regions with no scatter a new approach is required. We are the first to present a joint estimation algorithm based on Poisson data models for a single-scatter measurement geometry. Monotonic reduction of the log-likelihood function is guaranteed for our iterative algorithm while alternating image updates. We also present a fast algorithm for computing the discrete BRT forward operator. Our generalized approach can incorporate both transmission and scatter measurements from multiple source-detector pairs. Transmission measurements resolve low-frequency ambiguity in the joint image estimation problem, while multiple scatter measurements resolve the attenuation image. The benefits of joint estimation, over single-image estimation, vary with problem scaling. Our results quantify these benefits and should inform design of future acquisition systems.