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We present the meshfree Mixed Collocation Method (MCM) to solve the monodomain model for numerical simulation of cardiac electrophysiology. We apply MCM to simulate cardiac electrical propagation in 2D tissue sheets and 3D tissue slabs as…

Electrocardiogram (ECG) is a widely used diagnostic tool for detecting heart conditions. Rare cardiac diseases may be underdiagnosed using traditional ECG analysis, considering that no training dataset can exhaust all possible cardiac…

Although auto-regressive models excel in natural language processing, they often struggle to generate diverse text and provide limited controllability. Non-auto-regressive methods could be an alternative but often produce degenerate outputs…

Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…

Echocardiography video is a primary modality for diagnosing heart diseases, but the limited data poses challenges for both clinical teaching and machine learning training. Recently, video generative models have emerged as a promising…

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build…

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…

Real-world data generation often involves certain geometries (e.g., graphs) that induce instance-level interdependence. This characteristic makes the generalization of learning models more difficult due to the intricate interdependent…

Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

This paper presents CQT-Diff, a data-driven generative audio model that can, once trained, be used for solving various different audio inverse problems in a problem-agnostic setting. CQT-Diff is a neural diffusion model with an architecture…

We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…

Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses…

Pulsative signals such as the electrocardiogram (ECG) are extensively collected as part of routine clinical care. However, noisy and poor-quality recordings are a major issue for signals collected using mobile health systems, decreasing the…

Accurate correspondence matching in coronary angiography images is crucial for reconstructing 3D coronary artery structures, which is essential for precise diagnosis and treatment planning of coronary artery disease (CAD). Traditional…

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…

The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…