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Differentiable Forward and Back-Projector for Rigid Motion Estimation in X-ray Imaging.

Xiao Jiang, Xin Wang, Ali Uneri

IEEE Transactions on Bio-Medical Engineering

|December 12, 2025

Summary

This study introduces a new framework for differentiable forward and back-projectors, enabling faster and more accurate gradient computation for rigid motion estimation in X-ray imaging. The method offers significant speedups and improved image quality in various applications.

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Area of Science:

Medical Imaging
Computational Imaging
Image Reconstruction

Background:

Rigid motion estimation in X-ray imaging is crucial for accurate image reconstruction and analysis.
Existing gradient computation methods for motion estimation can be computationally expensive and memory-intensive.
Differentiable projectors are essential for gradient-based optimization in medical imaging tasks.

Purpose of the Study:

To propose a novel framework for differentiable forward and back-projectors.
To enable scalable, accurate, and memory-efficient gradient computation for rigid motion estimation.
To provide a unified gradient computation scheme applicable to various projector types.

Main Methods:

Developed a general analytical gradient formulation for forward/backprojection in the continuous domain.

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Expressed gradients directly in terms of forward and back-projection operations for a unified scheme.

Implemented a discretized version with an acceleration strategy balancing speed and memory.

Main Results:

Achieved approximately 8x speedup in 2D/3D registration compared to existing methods while maintaining accuracy.
Enhanced image sharpness and structural fidelity in motion-compensated analytical reconstruction and CT geometry calibration.
Demonstrated significant efficiency advantages over gradient-free and gradient-based solutions on real phantom data.

Conclusions:

The proposed differentiable projectors facilitate effective and efficient gradient-based solutions for X-ray imaging.
This framework is particularly beneficial for tasks involving rigid motion estimation.
The method offers a scalable and accurate approach to gradient computation in medical imaging.