Integrating Deep Unfolding with Direct Diffusion Bridges for Computed Tomography Reconstruction

Computed Tomography (CT) is widely used in healthcare for detailed imaging. However, Low-dose CT, despite reducing radiation exposure, often results in images with compromised quality due to increased noise. Traditional methods, including preprocessing, post-processing, and model-based approaches that leverage physical principles, are employed to improve the quality of image reconstructions from noisy projections or sinograms. Recently, deep learning has significantly advanced the field, with diffusion models outperforming both traditional methods and other deep learning approaches. These models effectively merge deep learning with physics, serving as robust priors for the inverse problem in CT. However, they typically require prolonged computation times during sampling. This paper introduces the first approach to merge deep unfolding with Direct Diffusion Bridges (DDBs) for CT, integrating the physics into the network architecture and facilitating the transition from degraded to clean images by bypassing excessively noisy intermediate stages commonly encountered in diffusion models. Moreover, this approach includes a tailored training procedure that eliminates errors typically accumulated during sampling. The proposed approach requires fewer sampling steps and demonstrates improved fidelity metrics, outperforming many existing state-of-the-art techniques.

Adversarial Deep-Unfolding Network for MA-XRF Super-Resolution on Old Master Paintings Using Minimal Training Data

High-quality element distribution maps enable precise analysis of the material composition and condition of Old Master paintings. These maps are typically produced from data acquired through Macro X-ray fluorescence (MA-XRF) scanning, a non-invasive technique that collects spectral information. However, MA-XRF is often limited by a trade-off between acquisition time and resolution. Achieving higher resolution requires longer scanning times, which can be impractical for detailed analysis of large artworks. Super-resolution MA-XRF provides an alternative solution by enhancing the quality of MA-XRF scans while reducing the need for extended scanning sessions. This paper introduces a tailored super-resolution approach to improve MA-XRF analysis of Old Master paintings. Our method proposes a novel adversarial neural network architecture for MA-XRF, inspired by the Learned Iterative Shrinkage-Thresholding Algorithm. It is specifically designed to work in an unsupervised manner, making efficient use of the limited available data. This design avoids the need for extensive datasets or pre-trained networks, allowing it to be trained using just a single high-resolution RGB image alongside low-resolution MA-XRF data. Numerical results demonstrate that our method outperforms existing state-of-the-art super-resolution techniques for MA-XRF scans of Old Master paintings.

Enhancing super-resolution ultrasound localisation through multi-frame deconvolution exploiting spatiotemporal coherence

Super-resolution ultrasound imaging through microbubble (MB) localisation and tracking, also known as ultrasound localisation microscopy, allows non-invasive sub-diffraction resolution imaging of microvasculature in animals and humans. The number of MBs localised from the acquired contrast-enhanced ultrasound (CEUS) images and the localisation precision directly influence the quality of the resulting super-resolution microvasculature images. However, non-negligible noise present in the CEUS images can make localising MBs challenging. To enhance the MB localisation performance, we propose a Multi-Frame Deconvolution (MF-Decon) framework that can exploit the spatiotemporal coherence inherent in the CEUS data, with new spatial and temporal regularisers designed based on total variation (TV) and regularisation by denoising (RED). Based on the MF-Decon framework, we introduce two novel methods: MF-Decon with spatial and temporal TVs (MF-Decon+3DTV) and MF-Decon with spatial RED and temporal TV (MF-Decon+RED+TV). Results from in silico simulations indicate that our methods outperform two widely used methods using deconvolution or normalised cross-correlation across all evaluation metrics, including precision, recall, $F_1$ score, mean and standard localisation errors. In particular, our methods improve MB localisation precision by up to 39% and recall by up to 12%. Super-resolution microvasculature maps generated with our methods on a publicly available in vivo rat brain dataset show less noise, better contrast, higher resolution and more vessel structures.

A Fast Automatic Method for Deconvoluting Macro X-ray Fluorescence Data Collected from Easel Paintings

Macro X-ray Fluorescence (MA-XRF) scanning is increasingly widely used by researchers in heritage science to analyse easel paintings as one of a suite of non-invasive imaging techniques. The task of processing the resulting MA-XRF datacube generated in order to produce individual chemical element maps is called MA-XRF deconvolution. While there are several existing methods that have been proposed for MA-XRF deconvolution, they require a degree of manual intervention from the user that can affect the final results. The state-of-the-art AFRID approach can automatically deconvolute the datacube without user input, but it has a long processing time and does not exploit spatial dependency. In this paper, we propose two versions of a fast automatic deconvolution (FAD) method for MA-XRF datacubes collected from easel paintings with ADMM (alternating direction method of multipliers) and FISTA (fast iterative shrinkage-thresholding algorithm). The proposed FAD method not only automatically analyses the datacube and produces element distribution maps of high-quality with spatial dependency considered, but also significantly reduces the running time. The results generated on the MA-XRF datacubes collected from two easel paintings from the National Gallery, London, verify the performance of the proposed FAD method.