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We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
LiDAR perception is severely limited by the distance-dependent sparsity of distant objects. While diffusion models can recover dense geometry, they suffer from prohibitive latency and physical hallucinations manifesting as ghost points. We…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
Recovering ghost-free High Dynamic Range (HDR) images from multiple Low Dynamic Range (LDR) images becomes challenging when the LDR images exhibit saturation and significant motion. Recent Diffusion Models (DMs) have been introduced in HDR…
Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to…
In analogy with the Poisson summation formula, we identify when the fractional Fourier transform, applied to a Dirac comb in dimension one, gives a discretely supported measure. We describe the resulting series of complex multiples of delta…
We introduce abstract rendering, a method for computing a set of images by rendering a scene from a continuously varying range of camera positions. The resulting abstract image-which encodes an infinite collection of possible renderings-is…
Two transformation-optics inspired flat lenses are used to build up an optical system capable to transpose an area surrounding the object focal point in a magnified area surrounding the image focal point. The object and image focal points…
Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities,…
Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…
Recent years have witnessed the remarkable success of implicit neural representation methods. The recent work Local Implicit Image Function (LIIF) has achieved satisfactory performance for continuous image representation, where pixel values…
We present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…
We present a fast and accurate method for dense depth reconstruction from sparsely sampled light fields obtained using a synchronized camera array. In our method, the source images are over-segmented into non-overlapping compact superpixels…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
Diffusion models learn to reverse the progressive noising of a data distribution to create a generative model. However, the desired continuous nature of the noising process can be at odds with discrete data. To deal with this tension…
Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
We propose a novel multi-stage depth super-resolution network, which progressively reconstructs high-resolution depth maps from explicit and implicit high-frequency features. The former are extracted by an efficient transformer processing…