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The proposed method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. Impulse HSPs were…
Echocardiography (ECHO) video is widely used for cardiac examination. In clinical, this procedure heavily relies on operator experience, which needs years of training and maybe the assistance of deep learning-based systems for enhanced…
Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters,…
Recently, the explicit constraint force method (ECFM) was introduced as a principled approach to solution reconstruction in the presence of missing physics. In solution reconstruction, parameters of a physical model are estimated from…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…
This paper presents a mathematical framework for a flexible pressure-sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface…
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the…
Cardiovascular signals such as photoplethysmography (PPG), electrocardiography (ECG), and blood pressure (BP) are inherently correlated and complementary, together reflecting the health of cardiovascular system. However, their joint…
Recent developments in application of deep learning models to acoustic Full Waveform Inversion (FWI) are marked by the use of diffusion models as prior distributions for Bayesian-like inference procedures. The advantage of these methods is…
This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…
Metasurfaces are ultra-thin optical elements composed of engineered sub-wavelength structures that enable precise control of light. Their inverse design - determining a geometry that yields a desired optical response - is challenging due to…
Image super-resolution is a fundamentally ill-posed problem because multiple valid high-resolution images exist for one low-resolution image. Super-resolution methods based on diffusion probabilistic models can deal with the ill-posed…
Electrocardiography (ECG) is a low-cost, widely used modality for diagnosing electrical abnormalities like atrial fibrillation by capturing the heart's electrical activity. However, it cannot directly measure cardiac morphological…
Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object…
Generative models, including denoising diffusion models (DM), are gaining attention in wireless applications due to their ability to learn complex data distributions. In this paper, we propose CoDiPhy, a novel framework that leverages…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
Electrocardiogram (ECG) is a widely used non-invasive diagnostic tool for heart diseases. Many studies have devised ECG analysis models (e.g., classifiers) to assist diagnosis. As an upstream task, researches have built generative models to…
In real-world clinical practice, electrocardiograms (ECGs) are often captured and shared as photographs. However, publicly available ECG data, and thus most related research, relies on digital signals. This has led to a disconnect in which…