Differentiable Uncalibrated Imaging

TL;DR

This paper introduces a differentiable imaging framework that jointly calibrates measurement uncertainties and reconstructs images, improving accuracy in 2D and 3D computed tomography.

Contribution

It develops a novel differentiable approach using neural fields and spline interpolators to handle measurement uncertainty in imaging.

Findings

Improved image reconstructions over baseline methods.

Effective joint calibration and reconstruction in CT imaging.

Framework adaptable to various imaging problems.

Abstract

We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the forward operator. To solve it we apply implicit neural networks, also known as neural fields, which are naturally differentiable with respect to the input coordinates. We also develop differentiable spline interpolators which perform as well as neural networks, require less time to optimize and have well-understood properties. Differentiability is key as it allows us to jointly fit a measurement representation, optimize over the uncertain measurement coordinates, and perform image reconstruction which in turn ensures consistent calibration. We apply our approach to 2D and 3D computed tomography, and show that it produces improved reconstructions compared to baselines that do not account for the lack of calibration. The flexibility of the proposed framework makes it easy to extend to almost arbitrary imaging problems.