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As the rapid growth of high-speed and deep-tissue imaging in biomedical research, it is urgent to find a robust and effective denoising method to retain morphological features for further texture analysis and segmentation. Conventional…

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…

We propose a novel approach to denoising diffusion magnetic resonance images (dMRI) using convolutional neural networks, that exploits the benefits of data acquired at multiple b-values to offset the need for many redundant observations.…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Many spectral CT applications require accurate material decomposition. Existing material decomposition algorithms are often susceptible to significant noise magnification or, in the case of one-step model-based approaches, hampered by slow…

The prevalence of digital sensors, such as digital cameras and mobile phones, simplifies the acquisition of photos. Digital sensors, however, suffer from producing Moire when photographing objects having complex textures, which deteriorates…

We prove a regularization by noise phenomenon for semilinear SPDEs driven by multiplicative cylindrical Brownian motion and singular diffusion coefficient. The analysis is based on a combination of infinite dimensional generalizations of…

We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to…

Nowadays, many applications rely on images of high quality to ensure good performance in conducting their tasks. However, noise goes against this objective as it is an unavoidable issue in most applications. Therefore, it is essential to…

In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…

We explore means to advance source camera identification based on sensor noise in a data-driven framework. Our focus is on improving the sensor pattern noise (SPN) extraction from a single image at test time. Where existing works suppress…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…

We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…

Spectroscopic photoacoustic (sPA) imaging uses multiple wavelengths to differentiate chromophores based on their unique optical absorption spectra. This technique has been widely applied in areas such as vascular mapping, tumor detection,…

Deep learning on an edge device requires energy efficient operation due to ever diminishing power budget. Intentional low quality data during the data acquisition for longer battery life, and natural noise from the low cost sensor degrade…

The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Although Monte Carlo and vanilla Physics-Informed Neural…

In typical single-pixel detection multiplexing, an unknown object is sequentially illuminated with intensity patterns: the total signal is summed into a single-pixel detector and is then demultiplexed to retrieve the object. Because of…