Data-Driven Filter Design for Flexible and Noise-Robust Tomographic Imaging

TL;DR

This paper introduces a data-driven method for learning FBP filters and projection weights to enhance robustness and adaptivity in tomographic imaging, outperforming traditional methods in noisy and incomplete data scenarios.

Contribution

It presents a novel optimization-based approach for learning adaptive FBP filters that improve noise robustness and generalize across different geometries and data types.

Findings

Learned filters improve image quality over traditional FBP and FDK.

Method adapts to noise levels and scan geometries.

Filters trained on synthetic data generalize well to real measurements.

Abstract

While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a data-driven approach for learning FBP filters and projection weights directly from training data, with the goal of improving robustness without sacrificing computational efficiency. The resulting reconstructions adapt naturally to the noise level and acquisition geometry, while retaining the speed and simplicity of classical back-projection. The proposed method can be formulated as a regularized optimization problem for a linear inverse operator, which allows us to establish existence, uniqueness, and stability of the learned solution. From a spectral viewpoint, the learned filters act as data-adaptive gain functions that explicitly balance noise amplification and bias, in close analogy to a regularized pseudo-inverse. Experiments in both 2D and 3D show consistent improvements over conventional FBP and FDK in different case studies. Finally, we show that filters trained on synthetic laminography data generalize well to real-world measurements, delivering image quality comparable to advanced iterative methods without the high computational cost.