Transformer Causality Regularization for Dynamic Inverse Problems

TL;DR

This paper introduces transformer causality regularization (TCR), a novel method combining transformer-based causality modeling with variational regularization to improve solutions of dynamic inverse problems, demonstrated on tomography data.

Contribution

The paper proposes TCR, integrating transformer causality priors with classical regularization, enhancing dynamic inverse problem solutions with theoretical convergence guarantees.

Findings

TCR improves reconstruction accuracy over static methods.

TCR enhances data consistency in dynamic tomography.

Transformer causality effectively models temporal dependencies.

Abstract

We study the concept of including the causality principle as regularizer into the solution of linear time-dependent inverse problems. This is achieved by combining transformer-based predictions with classical variational regularization, resulting in what we call transformer causality regularization (TCR). The causality principle states that an object at time $t'$ depends only on its previous states at $t < t'$ and is independent of future states at $t > t'$. Since the transformer architecture represents sequence-to-sequence functions and can be equipped with a causal attention mask, transformers are the natural choice for a learned causality function that predicts the state of an object at time $t'$ given the previous states at $t < t'$. We combine this with the inductive bias of convolutional neural networks (CNNs) for imaging tasks to treat the spatial variable. The output of the spatial-temporal transformer is then used as a prior for variational regularization, such that classical results on regularization and convergence for solution methods directly transfer to our case. Using the example of dynamic computerized tomography, we compare TCR to a static and dynamic version of the earlier introduced unrolled adversarial regularizer for simulated and measured data. The results show that using TCR within a variational framework improves reconstruction results and data-consistency.