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In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can…

Electrical impedance tomography (EIT) is a non-invasive imaging technique, which has been widely used in the fields of industrial inspection, medical monitoring and tactile sensing. However, due to the inherent non-linearity and…

Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently…

In this paper we consider the problem of acoustic inversion in the context of the optoacoustic tomography image reconstruction problem. By leveraging the ability of the recently proposed diffusion models for image generative tasks among…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness…

Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…

Electron microscopy (EM) images exhibit anisotropic axial resolution due to the characteristics inherent to the imaging modality, presenting challenges in analysis and downstream tasks.In this paper, we propose a diffusion-model-based…

Cardiac digital twins (CDTs) are personalized virtual representations used to understand complex cardiac mechanisms. A critical component of CDT development is solving the ECG inverse problem, which enables the reconstruction of cardiac…

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

Traditional elastic wavefield separation methods, while accurate, often demand substantial computational resources, especially for large geological models or 3D scenarios. Purely data-driven neural network approaches can be more efficient,…

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…

Objective: Decoding visual information from electroencephalography (EEG) is an important problem in neuroscience and brain-computer interface (BCI) research. Existing methods are largely restricted to natural images and categorical…

Cardiac computed tomography (CT) has emerged as a major imaging modality for the diagnosis and monitoring of cardiovascular diseases. High temporal resolution is essential to ensure diagnostic accuracy. Limited-angle data acquisition can…

Modeling cardiovascular anatomies poses a significant challenge due to their complex, irregular structures and inherent pathological conditions. Numerical simulations, while accurate, are often computationally expensive, limiting their…

We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related…

Magnetic resonance (MR) imaging, including cardiac MR, is prone to domain shift due to variations in imaging devices and acquisition protocols. This challenge limits the deployment of trained AI models in real-world scenarios, where…

Modeling the behavior of biological tissues and organs often necessitates the knowledge of their shape in the absence of external loads. However, when their geometry is acquired in-vivo through imaging techniques, bodies are typically…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…