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In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
As vision based perception methods are usually built on the normal light assumption, there will be a serious safety issue when deploying them into low light environments. Recently, deep learning based methods have been proposed to enhance…
We study an adaptive anisotropic Huber functional based image restoration scheme. By using a combination of L2-L1 regularization functions, an adaptive Huber functional based energy minimization model provides denoising with edge…
Radial correction distortion, applied by in-camera or out-camera software/firmware alters the supporting grid of the image so as to hamper PRNU-based camera attribution. Existing solutions to deal with this problem try to invert/estimate…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
We present a simple, yet effective diffusion-based method for fine-grained, parametric control over light sources in an image. Existing relighting methods either rely on multiple input views to perform inverse rendering at inference time,…
Underwater imagery often exhibits distorted coloration as a result of light-water interactions, which complicates the study of benthic environments in marine biology and geography. In this research, we propose an algorithm to restore the…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We propose a method that combines sparse depth (LiDAR) measurements with an intensity image and to produce a dense high-resolution depth image. As there are few, but accurate, depth measurements from the scene, our method infers the…
Imaging through dense fog presents unique challenges, with essential visual information crucial for applications like object detection and recognition obscured, thereby hindering conventional image processing methods. Despite improvements…
Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models…
Images captured in low-light conditions usually suffer from very low contrast, which increases the difficulty of subsequent computer vision tasks in a great extent. In this paper, a low-light image enhancement model based on convolutional…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown…
In this paper, we propose a 2-stage low-light image enhancement method called Self-Reference Deep Adaptive Curve Estimation (Self-DACE). In the first stage, we present an intuitive, lightweight, fast, and unsupervised luminance enhancement…
When one captures images in low-light conditions, the images often suffer from low visibility. This poor quality may significantly degrade the performance of many computer vision and multimedia algorithms that are primarily designed for…
Images captured in low-light environment often suffer from complex degradation. Simply adjusting light would inevitably result in burst of hidden noise and color distortion. To seek results with satisfied lighting, cleanliness, and realism…