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Super-resolution of turbulence is a term used to describe the prediction of high-resolution snapshots of a flow from coarse-grained observations. This is typically accomplished with a deep neural network and training usually requires a…
Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…
In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…
Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only be partially known or inaccurately modeled, images may not be well restored. Rain streak…
Image registration is one important task in many image processing applications. It aims to align two or more images so that useful information can be extracted through comparison, combination or superposition. This is achieved by…
Atmospheric optical turbulence can be a significant source of image degradation, particularly in long range imaging applications. Many turbulence mitigation algorithms rely on an optical transfer function (OTF) model that includes the Fried…
A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial…
We present a framework for inferring an atmospheric transmission profile from a spectral scene. This framework leverages a lightweight, physics-based simulator that is automatically tuned - by virtue of autodifferentiation and…
The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse…
We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts,…
We propose a multi-model formulation of full-waveform inversion that is similar to image decomposition into a "cartoon" and "texture" used in image processing. Inversion problem is formulated as unconstrained multi-norm optimization that…
In this work, we extract the optical flow field corresponding to moving objects from an image sequence of a scene impacted by atmospheric turbulence \emph{and} captured from a moving camera. Our procedure first computes the optical flow…
The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation…
We consider an inverse flow problem in which the airfoil shape is identified from its wake signature, namely the velocity field in the wake of a target airfoil. This is an ill-posed problem and highly sensitive to the accuracy and…
A central problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence…
We present a learning-based approach for removing unwanted obstructions, such as window reflections, fence occlusions, or adherent raindrops, from a short sequence of images captured by a moving camera. Our method leverages motion…
Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in…
We present HyperMorph, a learning-based strategy for deformable image registration that removes the need to tune important registration hyperparameters during training. Classical registration methods solve an optimization problem to find a…
Robust invisible watermarking aims to embed hidden information into images such that the watermark can survive various image manipulations. However, the rise of powerful diffusion-based image generation and editing techniques poses a new…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…