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We propose a new technique for estimating spatially varying parametric materials from a single image of an object with unknown shape in unknown illumination. Our method uses a low-order parametric reflectance model, and incorporates strong…
As a widely recognized approach to deep generative modeling, Variational Auto-Encoders (VAEs) still face challenges with the quality of generated images, often presenting noticeable blurriness. This issue stems from the unrealistic…
One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern…
Wavefront shaping systems aim to image deep into scattering tissue by reshaping incoming and outgoing light to correct aberrations caused by tissue inhomogeneity However, the desired modulation depends on the unknown tissue structure and…
Optimal computations under uncertainty require an adequate probabilistic representation about beliefs. Deep generative models, and specifically Variational Autoencoders (VAEs), have the potential to meet this demand by building latent…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We propose a novel intrinsic image decomposition network considering reflectance consistency. Intrinsic image decomposition aims to decompose an image into illumination-invariant and illumination-variant components, referred to as…
Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
Colorization is an ambiguous problem, with multiple viable colorizations for a single grey-level image. However, previous methods only produce the single most probable colorization. Our goal is to model the diversity intrinsic to the…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…
We introduce deep learning based communication methods for successive refinement of images over wireless channels. We present three different strategies for progressive image transmission with deep JSCC, with different…
Wave-based imaging techniques use wavefield data from receivers on the boundary of a domain to produce an image of the underlying structure in the domain of interest. These images are defined by the imaging condition, which maps recorded…
This paper introduces a novel method for image colorization that utilizes a color transformer and generative adversarial networks (GANs) to address the challenge of generating visually appealing colorized images. Conventional approaches…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…