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Many inverse problems in physics are particularly challenging due to their ill-posed nature and high complexity. We tackle these challenges using physics-informed machine learning (ML) algorithms, invertible neural networks (INNs), and likelihood-based generative models, including conditional normalizing flows (cNFs). First, the physics-informed ML incorporates physical models into neural networks (NNs) to address the challenge of limited experimental ground-truth datasets. For instance, in phase retrieval for X-ray holography, integrating the physics of image formation or wave propagation into calculating the loss function allows for automatic optimization to produce the desired solution. Second, cNFs enable us to learn the full distribution of target parameters, capturing all possible solutions. This contrasts with classical neural networks and conventional algorithms, which often struggle with undetermined inverse problems, leading to ambiguities by predicting only a single or an average solution. In X-Ray and Neutron Reflectometry (XRR and NR), this helps distinguish between different thin film parameter sets that produce identical reflectivity curves caused by limited phase information. We demonstrate, that our approaches successfully integrate ML to guide experimental design, optimize parameters, and enhance solutions for inverse problems, with applications in laser-plasma interactions, X-ray imaging, and related techniques. This highlights the potential of ML to advance research and overcome limitations in complex physical simulations and experiments.

Phase retrieval is an ill-posed inverse problem with several applications in the fields of medical imaging and materials science. Conventional phase retrieval algorithms either simplify the problem by assuming certain object properties and optical propagation regimes or tuning a large number of free parameters. While the latter most often leads to good solutions for a wider application range, it is still a time-consuming process, even for experienced users. One way to circumvent this is by introducing a self-optimizing machine learning- based algorithm. Basing this on invertible networks such as normalising flows ensures good inversion, effi- cient sampling, and fast probability density estimation for large images and generally, complex-valued dis- tributions. Here, complex wavefield datasets are trained and tested on a normalising flows-based machine learning model for phase retrieval called conditional Wavelet Flow (cWF) and benchmarked against other conventional algorithms and baseline models. The cWF algorithm adds a conditioning network on top of the Wavelet Flow algorithm that is able to model the conditional data distribution of high resolution images of up to 1024 x 1024 pixels, which was not possible in other flow-based models. Additionally, cWF takes advantage of the parallelized training of different image resolutions, allowing for more efficient and fast training of large datasets. The trained algorithm is then applied to X-ray holography data wherein fast and high-quality image reconstruction is made possible.

Phase retrieval is an ill-posed inverse problem with several applications in the fields of medical imaging and materials science. Conventional phase retrieval algorithms either simplify the problem by assuming certain object properties and optical propagation regimes or tuning a large number of free parameters. While the latter most often leads to good solutions for a wider application range, it is still a time-consuming process, even for experienced users. One way to circumvent this is by introducing a self-optimizing machine learning- based algorithm. Basing this on invertible networks such as normalising flows ensures good inversion, effi- cient sampling, and fast probability density estimation for large images and generally, complex-valued dis- tributions. Here, complex wavefield datasets are trained and tested on a normalising flows-based machine learning model for phase retrieval called conditional Wavelet Flow (cWF) and benchmarked against other conventional algorithms and baseline models. The cWF algorithm adds a conditioning network on top of the Wavelet Flow algorithm that is able to model the conditional data distribution of high resolution images of up to 1024 x 1024 pixels, which was not possible in other flow-based models. Additionally, cWF takes advantage of the parallelized training of different image resolutions, allowing for more efficient and fast training of large datasets. The trained algorithm is then applied to X-ray holography data wherein fast and high-quality image reconstruction is made possible.

Characterizing nanoparticles (NPs) distribution in multiple and complex metastases is of fundamental relevance for the development of radiological protocols based on NPs administration. In the literature, there have been advances in monitoring NPs in tissues. However, the lack of 3D information is still an issue. X-ray phase-contrast tomography (XPCT) is a 3D label-free, non-invasive and multi-scale approach allowing imaging anatomical details with high spatial and contrast resolutions. Here an XPCT qualitative study on NPs distribution in a mouse brain model of melanoma metastases injected with gadolinium-based NPs for theranostics is presented. For the first time, XPCT images show the NPs uptake at micrometer resolution over the full brain. Our results revealed a heterogeneous distribution of the NPs inside the melanoma metastases, bridging the gap in spatial resolution between magnetic resonance imaging and histology. Our findings demonstrated that XPCT is a reliable technique for NPs detection and can be considered as an emerging method for the study of NPs distribution in organs.

Characterizing nanoparticles (NPs) distribution in multiple and complex metastases is of fundamental relevance for the development of radiological protocols based on NPs administration. In the literature, there have been advances in monitoring NPs in tissues. However, the lack of 3D information is still an issue. X-ray phase-contrast tomography (XPCT) is a 3D label-free, non-invasive and multi-scale approach allowing imaging anatomical details with high spatial and contrast resolutions. Here an XPCT qualitative study on NPs distribution in a mouse brain model of melanoma metastases injected with gadolinium-based NPs for theranostics is presented. For the first time, XPCT images show the NPs uptake at micrometer resolution over the full brain. Our results revealed a heterogeneous distribution of the NPs inside the melanoma metastases, bridging the gap in spatial resolution between magnetic resonance imaging and histology. Our findings demonstrated that XPCT is a reliable technique for NPs detection and can be considered as an emerging method for the study of NPs distribution in organs.

X-ray computed tomography (CT) is an invaluable technique for generating three-dimensional (3D) images of inert or living specimens. X-ray CT is used in many scientific, industrial, and societal fields. Compared to conventional 2D X-ray imaging, CT requires longer acquisition times because up to several thousand projections are required for reconstructing a single high-resolution 3D volume. Plenoptic imaging—an emerging technology in visible light field photography—highlights the potential of capturing quasi-3D information with a single exposure. Here, we show the first demonstration of a flexible plenoptic microscope operating with hard X-rays; it is used to computationally reconstruct images at different depths along the optical axis. The experimental results are consistent with the expected axial refocusing, precision, and spatial resolution. Thus, this proof-of-concept experiment opens the horizons to quasi-3D X-ray imaging, without sample rotation, with spatial resolution of a few hundred nanometres.

X-ray computed tomography (CT) is an invaluable technique for generating three-dimensional (3D) images of inert or living specimens. X-ray CT is used in many scientific, industrial, and societal fields. Compared to conventional 2D X-ray imaging, CT requires longer acquisition times because up to several thousand projections are required for reconstructing a single high-resolution 3D volume. Plenoptic imaging—an emerging technology in visible light field photography—highlights the potential of capturing quasi-3D information with a single exposure. Here, we show the first demonstration of a flexible plenoptic microscope operating with hard X-rays; it is used to computationally reconstruct images at different depths along the optical axis. The experimental results are consistent with the expected axial refocusing, precision, and spatial resolution. Thus, this proof-of-concept experiment opens the horizons to quasi-3D X-ray imaging, without sample rotation, with spatial resolution of a few hundred nanometres.

Hard X-ray nanotomography enables 3D investigations of a wide range of samples with high resolution (<100 nm) with both synchrotron-based and laboratory-based setups. However, the advantage of synchrotron-based setups is the high flux, enabling time resolution, which cannot be achieved at laboratory sources. Here, the nanotomography setup at the imaging beamline P05 at PETRA III is presented, which offers high time resolution not only in absorption but for the first time also in Zernike phase contrast. Two test samples are used to evaluate the image quality in both contrast modalities based on the quantitative analysis of contrast-to-noise ratio (CNR) and spatial resolution. High-quality scans can be recorded in 15 min and fast scans down to 3 min are also possible without significant loss of image quality. At scan times well below 3 min, the CNR values decrease significantly and classical image-filtering techniques reach their limitation. A machine-learning approach shows promising results, enabling acquisition of a full tomography in only 6 s. Overall, the transmission X-ray microscopy instrument offers high temporal resolution in absorption and Zernike phase contrast, enabling in situ experiments at the beamline.

Hard X-ray nanotomography enables 3D investigations of a wide range of samples with high resolution (<100 nm) with both synchrotron-based and laboratory-based setups. However, the advantage of synchrotron-based setups is the high flux, enabling time resolution, which cannot be achieved at laboratory sources. Here, the nanotomography setup at the imaging beamline P05 at PETRA III is presented, which offers high time resolution not only in absorption but for the first time also in Zernike phase contrast. Two test samples are used to evaluate the image quality in both contrast modalities based on the quantitative analysis of contrast-to-noise ratio (CNR) and spatial resolution. High-quality scans can be recorded in 15 min and fast scans down to 3 min are also possible without significant loss of image quality. At scan times well below 3 min, the CNR values decrease significantly and classical image-filtering techniques reach their limitation. A machine-learning approach shows promising results, enabling acquisition of a full tomography in only 6 s. Overall, the transmission X-ray microscopy instrument offers high temporal resolution in absorption and Zernike phase contrast, enabling in situ experiments at the beamline.