Related papers: Parameter learning and fractional differential ope…

We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev…

The difficulty of obtaining paired data remains a major bottleneck for learning image restoration and enhancement models for real-world applications. Current strategies aim to synthesize realistic training data by modeling noise and…

The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE…

The Transformer translation model employs residual connection and layer normalization to ease the optimization difficulties caused by its multi-layer encoder/decoder structure. Previous research shows that even with residual connection and…

Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to partial differential equations (PDEs). However, they still…

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

Recently, deep learning methods such as the convolutional neural networks have gained prominence in the area of image denoising. This is owing to their proven ability to surpass state-of-the-art classical image denoising algorithms such as…

Hyperspectral images (HSIs) are inevitably degraded by a mixture of various types of noise, such as Gaussian noise, impulse noise, stripe noise, and dead pixels, which greatly limits the subsequent applications. Although various denoising…

Optical neural networks are emerging as powerful machine learning and information processing tools because of their potential advantages in speed and energy efficiency. The training methods of these physical models, however, remain…

Spatially varying regularization accommodates the deformation variations that may be necessary for different anatomical regions during deformable image registration. Historically, optimization-based registration models have harnessed…

In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…

A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…

During the acquisition of an image from its source, noise always becomes an integral part of it. Various algorithms have been used in past to denoise the images. Image denoising still has scope for improvement. Visual information…

Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling…

We propose and experimentally demonstrate an efficient image decomposition in the Laguerre-Gaussian (LG) domain. By developing an advanced computing method, the sampling points are much fewer than those in the existing methods, which can…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

We investigate an approach for the numerical solution of differential equations which is based on the perfect discretization of actions. Such perfect discretizations show up at the fixed points of renormalization group transformations. This…

We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…

Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while…

Natural image matting, which separates foreground from background, is a very important intermediate step in recent computer vision algorithms. However, it is severely underconstrained and difficult to solve. State-of-the-art approaches…