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This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Path-length diversity methods may be used for adaptive optics (AO) systems to retrieve phase and amplitude information by measuring intensity across multiple planes. Observations that rely on free-space propagation, such as the nonlinear…
Shading-based approaches like Photometric Stereo assume that the image formation model can be effectively optimized for the scene normals. However, in murky water this is a very challenging problem. The light from artificial sources is not…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
Non-invasive detection of objects embedded inside an optically scattering medium is essential for numerous applications in engineering and sciences. However, in most applications light at visible or near-infrared wavebands is scattered by…
Non-line-of-sight (NLOS) imaging techniques use light that diffusely reflects off of visible surfaces (e.g., walls) to see around corners. One approach involves using pulsed lasers and ultrafast sensors to measure the travel time of…
Brillouin-Mandelstam scattering is one of the most accessible nonlinear optical phenomena and has been widely studied since its theoretical discovery one hundred years ago. The scattering mechanism is a three-wave-mixing process between two…
We develop an ultrawideband (UWB) inverse scattering technique for reconstructing continuous random media based on Bayesian compressive sensing. In addition to providing maximum a posteriori estimates of the unknown weights, Bayesian…
Strong-lensing images provide a wealth of information both about the magnified source and about the dark matter distribution in the lens. Precision analyses of these images can be used to constrain the nature of dark matter. However, this…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
3D Gaussian Splatting (3DGS) is a powerful reconstruction technique, but it needs to be initialized from accurate camera poses and high-fidelity point clouds. Typically, the initialization is taken from Structure-from-Motion (SfM)…
Images of static scenes submerged beneath a wavy water surface exhibit severe non-rigid distortions. The physics of water flow suggests that water surfaces possess spatio-temporal smoothness and temporal periodicity. Hence they possess a…
Recent efforts in using 3D Gaussians for scene reconstruction and novel view synthesis can achieve impressive results on curated benchmarks; however, images captured in real life are often blurry. In this work, we analyze the robustness of…
Reliable estimation and approximation of probability density functions is fundamental for their further processing. However, their specific properties, i.e. scale invariance and relative scale, prevent the use of standard methods of spline…
We consider the statistical inverse problem of estimating a background fluid flow field $\mathbf{v}$ from the partial, noisy observations of the concentration $\theta$ of a substance passively advected by the fluid, so that $\theta$ is…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Lensless imaging offers a lightweight, compact alternative to traditional lens-based systems, ideal for exploration in space-constrained environments. However, the absence of a focusing lens and limited lighting in such environments often…