Ultralow‐parameter denoising: Trainable bilateral filter layers in computed tomography

Abstract

Background Computed tomography (CT) is widely used as an imaging tool to visualize three‐dimensional structures with expressive bone‐soft tissue contrast. However, CT resolution can be severely degraded through low‐dose acquisitions, highlighting the importance of effective denoising algorithms. Purpose Most data‐driven denoising techniques are based on deep neural networks, and therefore, contain hundreds of thousands of trainable parameters, making them incomprehensible and prone to prediction failures. Developing understandable and robust denoising algorithms achieving state‐of‐the‐art performance helps to minimize radiation dose while maintaining data integrity. Methods This work presents an open‐source CT denoising framework based on the idea of bilateral filtering. We propose a bilateral filter that can be incorporated into any deep learning pipeline and optimized in a purely data‐driven way by calculating the gradient flow toward its hyperparameters and its input. Denoising in pure image‐to‐image pipelines and across different domains such as raw detector data and reconstructed volume, using a differentiable backprojection layer, is demonstrated. In contrast to other models, our bilateral filter layer consists of only four trainable parameters and constrains the applied operation to follow the traditional bilateral filter algorithm by design. Results Although only using three spatial parameters and one intensity range parameter per filter layer, the proposed denoising pipelines can compete with deep state‐of‐the‐art denoising architectures with several hundred thousand parameters. Competitive denoising performance is achieved on x‐ray microscope bone data and the 2016 Low Dose CT Grand Challenge data set. We report structural similarity index measures of 0.7094 and 0.9674 and peak signal‐to‐noise ratio values of 33.17 and 43.07 on the respective data sets. Conclusions Due to the extremely low number of trainable parameters with well‐defined effect, prediction reliance and data integrity is guaranteed at any time in the proposed pipelines, in contrast to most other deep learning‐based denoising architectures.

Calibration by differentiation – Self‐supervised calibration for X‐ray microscopy using a differentiable cone‐beam reconstruction operator

“…Hence, in our case, the minimization of the TV norm needs to be achieved by cupping correction rather than noise reduction. It has already been demonstrated that incorporating a denoiser based on supervised learning into the proposed pipeline yields state‐of‐the‐art results 49 . Investigating a joint denoising and cupping correction approach can be an interesting avenue for future work.…”

“…It has already been demonstrated that incorporating a denoiser based on supervised learning into the proposed pipeline yields state-of-the-art results. 49 Investigating a joint denoising and cupping correction approach can be an interesting avenue for future work.…”

Deep learning for terahertz image denoising in nondestructive historical document analysis

“…In this work, some exemplary results of other algorithms are also displayed as a comparison. The bilateral filter 47 and its trainable version 48 are applied to compare with well-known adaptive www.nature.com/scientificreports/ filters. In particular trainable bilateral filter versions have been shown to provide robust denoising performance in the context of medical imaging 49 .…”

“…Noise2Self and Noise2Void are well-known self-supervised denoising algorithms. In our experiments, three trainable bilateral filter layers are trained in a self-supervised way using the Noise2Void method following the setup of Wagner et al 48 .…”

Trainable joint bilateral filters for enhanced prediction stability in low-dose CT

“…In our previous work, we presented a trainable bilateral filter with competitive denoising performance that can be included in a differentiable pipeline and optimized in a data-driven fashion 29 . However, the prediction of bilateral filter layers is solely dependent on three learned spatial parameters and one intensity parameter 9 .…”