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

• Published in: Journal of microscopy (Oxford) Vol. 287; no. 2; pp. 81 - 92
• Main Authors: Thies, Mareike, Wagner, Fabian, Huang, Yixing, Gu, Mingxuan, Kling, Lasse, Pechmann, Sabrina, Aust, Oliver, Grüneboom, Anika, Schett, Georg, Christiansen, Silke, Maier, Andreas
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.08.2022
• Subjects: Biomedical materials; Bone imaging; Bones; Calibration; Computed tomography; Data processing; Deep learning; Image contrast; Image quality; Image reconstruction; inverse problems; known operator learning; Mathematical analysis; Medical imaging; Microscopy; Modules; Osteoporosis; reconstruction; X‐ray microscopy; computed tomography; deep learning; reconstruction; X-ray microscopy; inverse problems; known operator learning
• ISSN: 0022-2720; 1365-2818
• DOI: 10.1111/jmi.13125

High‐resolution X‐ray microscopy (XRM) is gaining interest for biological investigations of extremely small‐scale structures. XRM imaging of bones in living mice could provide new insights into the emergence and treatment of osteoporosis by observing osteocyte lacunae, which are holes in the bone of few micrometres in size. Imaging living animals at that resolution, however, is extremely challenging and requires very sophisticated data processing converting the raw XRM detector output into reconstructed images. This paper presents an open‐source, differentiable reconstruction pipeline for XRM data which analytically computes the final image from the raw measurements. In contrast to most proprietary reconstruction software, it offers the user full control over each processing step and, additionally, makes the entire pipeline deep learning compatible by ensuring differentiability. This allows fitting trainable modules both before and after the actual reconstruction step in a purely data‐driven way using the gradient‐based optimizers of common deep learning frameworks. The value of such differentiability is demonstrated by calibrating the parameters of a simple cupping correction module operating on the raw projection images using only a self‐supervisory quality metric based on the reconstructed volume and no further calibration measurements. The retrospective calibration directly improves image quality as it avoids cupping artefacts and decreases the difference in grey values between outer and inner bone by 68–94%. Furthermore, it makes the reconstruction process entirely independent of the XRM manufacturer and paves the way to explore modern deep learning reconstruction methods for arbitrary XRM and, potentially, other flat‐panel computed tomography systems. This exemplifies how differentiable reconstruction can be leveraged in the context of XRM and, hence, is an important step towards the goal of reducing the resolution limit of in vivo bone imaging to the single micrometre domain. Lay description X‐ray microscopy (XRM) is an imaging modality that non‐destructively acquires 3D images of very high resolution. Applied to the bones of living mice, this could yield new insights into the change of small bony structures when the animal is infected with osteoporosis. However, acquiring artifact‐free images of living mice is very challenging. Consequently, powerful data processing is needed to resolve the structures of interest. We present a complete XRM reconstruction algorithm which converts the detector signal into interpretable volumetric images. Our pipeline lets the user adjust and augment the reconstruction to the needs of the given application and even allows to incorporate trainable components such as deep networks. These can flexibly be inserted into the pipeline and learned from data. To demonstrate this, we optimize the few free parameters of a cupping correction module. It reduces prominent intensity differences in the reconstructed bones without the need for any additional measurements. This exemplifies how the proposed pipeline increases the quality of the obtained reconstructions. Overall, our method is a tool enabling flexible, state‐of‐the‐art XRM data processing in order to pave the way toward future in‐vivo experiments. The source code and data are publicly available at https://doi.org/10.24433/CO.2740182.v2.