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We propose a new method, Patch-CNN, for diffusion tensor (DT) estimation from only six-direction diffusion weighted images (DWI). Deep learning-based methods have been recently proposed for dMRI parameter estimation, using either voxel-wise…

Optical coherence tomography (OCT) is a prevalent non-invasive imaging method which provides high resolution volumetric visualization of retina. However, its inherent defect, the speckle noise, can seriously deteriorate the tissue…

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…

Motivated through various applications of the trapping diffusion-influenced reactions theory in physics, chemistry and biology, this paper deals with irreducible Cartesian tensors (ICT) technique within the scope of the generalized method…

We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…

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,…

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma:…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…

This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Intravoxel Incoherent Motion (IVIM) is a non-contrast magnetic resonance imaging diffusion-based scan that uses a multitude of b-values to measure various speeds of molecular perfusion and diffusion, sidestepping inaccuracy of arterial…

Diffusion magnetic resonance imaging datasets suffer from low Signal-to-Noise Ratio, especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and…

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…

Diffusion inversion aims to recover the initial noise corresponding to a given image such that this noise can reconstruct the original image through the denoising diffusion process. The key component of diffusion inversion is to minimize…

Limited-angle and sparse-view computed tomography (LACT and SVCT) are crucial for expanding the scope of X-ray CT applications. However, they face challenges due to incomplete data acquisition, resulting in diverse artifacts in the…

We propose a simple but effective training-free approach tailored to diffusion-based image-to-image translation. Our approach revises the original noise prediction network of a pretrained diffusion model by introducing a noise correction…

We present the first acquisition-agnostic diffusion generative model for Magnetic Resonance Imaging (MRI) in the neonatal intensive care unit (NICU) to solve a range of inverse problems for shortening scan time and improving motion…

Remote sensing semantic segmentation must address both what the ground objects are within an image and where they are located. Consequently, segmentation models must ensure not only the semantic correctness of large-scale patches…

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…