# Accurate, provable and fast polychromatic tomographic reconstruction: A variational inequality approach

arXiv: https://arxiv.org/abs/2503.19925 · HTML: https://mlsanity.com/paper/2503.19925/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 66 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [The estimation error of general first order methods](https://mlsanity.com/paper/2002.12903/) (2020)
- [Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization](https://mlsanity.com/paper/2207.09660/) (2022)
- [Convergence for nonconvex ADMM, with applications to CT imaging](https://mlsanity.com/paper/2006.07278/) (2020)
- [A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth](https://mlsanity.com/paper/2205.00064/) (2022)
- [Hyperparameter tuning via trajectory predictions: Stochastic prox-linear methods in matrix sensing](https://mlsanity.com/paper/2402.01599/) (2024)
- [Gradient Descent Provably Solves Nonlinear Tomographic Reconstruction](https://mlsanity.com/paper/2310.03956/) (2023)
- [Precise asymptotics of reweighted least-squares algorithms for linear diagonal networks](https://mlsanity.com/paper/2406.02769/) (2024)
- [MACE CT Reconstruction for Modular Material Decomposition from Energy Resolving Photon-Counting Data](https://mlsanity.com/paper/2402.00967/) (2024)
- [Nonlinear tomographic reconstruction via nonsmooth optimization](https://mlsanity.com/paper/2407.12984/) (2024)

## Built on by (most cited first, 3 of 3)

- [Beyond Maximum Likelihood: Variational Inequality Estimation for Generalized Linear Models](https://mlsanity.com/paper/2511.03087/) (2025)
- [Multiscale replay: A robust algorithm for stochastic variational inequalities with a Markovian buffer](https://mlsanity.com/paper/2601.01502/) (2026)
- [Perfusion Imaging and Single Material Reconstruction in Polychromatic Photon Counting CT](https://mlsanity.com/paper/2602.02713/) (2026)

## Abstract (arXiv)

We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot noise), and observations acquired over multiple wavelength windows. We develop a simple iterative algorithm for single-material reconstruction, which we call EXACT (EXtragradient Algorithm for Computed Tomography), based on formulating our estimate as the fixed point of a monotone variational inequality. We prove guarantees on the statistical and computational performance of EXACT under realistic assumptions on the measurement process. We also consider a recently introduced variant of this model with Gaussian measurements and present sample and iteration complexity bounds for EXACT that improve upon those of existing algorithms. We apply our EXACT algorithm to a CT phantom image recovery task and show that it often requires fewer X-ray views, lower source intensity, and less computation time to achieve reconstruction quality similar to existing methods. Code is available at https://github.com/voilalab/exact.