Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data
| Autor: | Joseph A. O'Sullivan, Michael R. Walker |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Signal Processing (eess.SP)
Tomographic reconstruction Noise measurement Computer science Iterative method Attenuation Image and Video Processing (eess.IV) Function (mathematics) Electrical Engineering and Systems Science - Image and Video Processing Inverse problem 01 natural sciences 030218 nuclear medicine & medical imaging Computer Science Applications 010101 applied mathematics Reduction (complexity) 03 medical and health sciences Computational Mathematics 0302 clinical medicine Signal Processing FOS: Electrical engineering electronic engineering information engineering Electrical Engineering and Systems Science - Signal Processing 0101 mathematics Focus (optics) Algorithm |
| Zdroj: | IEEE Transactions on Computational Imaging. 7:361-374 |
| ISSN: | 2334-0118 2573-0436 |
| Popis: | 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. 13 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|