A Scalable Sequential Framework for Dynamic Inverse Problems via Model Parameter Estimation

TL;DR

This paper introduces a memory-efficient, sequential framework for dynamic inverse problems, specifically for reconstructing undersampled CT images, by integrating regularized motion models with Kalman filtering and EM for parameter estimation.

Contribution

It presents a novel, scalable approach combining Kalman filtering with EM to estimate model parameters in real-time, reducing memory use and hyperparameter tuning in dynamic inverse problems.

Findings

Improved reconstruction accuracy in limited-angle CT scenarios

Reduced memory and computational requirements

Effective online estimation of model parameters

Abstract

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and structural constraints. However, classical regularization formulations are frequently infeasible in this setting due to prohibitive memory requirements, necessitating sequential methods that process data and state information online, eliminating the need to form the full space-time problem. In this work, we propose a memory-efficient framework for reconstructing dynamic sequences of undersampled images from computerized tomography data that requires minimal hyperparameter tuning. The approach is based on a prior-informed, dimension-reduced Kalman filter with smoothing. While well suited for dynamic image reconstruction, practical deployment is challenging when the state transition model and covariance parameters must be initialized without prior knowledge and estimated in a single pass. To address these limitations, we integrate regularized motion models with expectation-maximization strategies for the estimation of state transition dynamics and error covariances within the Kalman filtering framework. We demonstrate the effectiveness of the proposed method through numerical experiments on limited-angle and single-shot computerized tomography problems, highlighting improvements in reconstruction accuracy, memory efficiency, and computational cost.