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Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
Objective:This study introduces a residual error-shifting mechanism that drastically reduces sampling steps while preserving critical anatomical details, thus accelerating MRI reconstruction. Approach:We propose a novel diffusion-based SR…
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard…
Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…
Diffusion tractography is routinely used to study white matter architecture and brain connectivity in vivo. A key step for successful tractography of neuronal tracts is the correct identification of tract directions in each voxel. Here we…
High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex neuronal fiber configurations, albeit, at the cost of long acquisition times. We propose a method to recover intra-voxel fiber…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
Diffusion kurtosis imaging is an extension of diffusion tensor imaging that provides scientifically and clinically valuable information about brain tissue microstructure but suffers from poor robustness to noise, especially in voxels…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
Diffusion model (DM) based Video Super-Resolution (VSR) approaches achieve impressive perceptual quality. However, they suffer from error accumulation, spatial artifacts, and a trade-off between perceptual quality and fidelity, primarily…
Ultrasound-modulated optical tomography is an emerging biomedical imaging modality which uses the spatially localised acoustically-driven modulation of coherent light as a probe of the structure and optical properties of biological tissues.…
Low-field to high-field MRI synthesis has emerged as a cost-effective strategy to enhance image quality under hardware and acquisition constraints, particularly in scenarios where access to high-field scanners is limited or impractical.…
Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posedness of the inverse problem poses a huge challenge to FMT reconstruction. Although end-to-end deep…
High resolution diffusion MRI (dMRI) data is often constrained by limited scanning time in clinical settings, thus restricting the use of downstream analysis techniques that would otherwise be available. In this work we develop a 3D…
Diffusion MRI is a neuroimaging technique measuring the anatomical structure of tissues. Using diffusion MRI to construct the connections of tissues, known as fiber tracking, is one of the most important uses of diffusion MRI. Many…
Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized…
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…