Related papers: Explainable bilevel optimization: an application t…
Variational models for image deblurring problems typically consist of a smooth term and a potentially non-smooth convex term. A common approach to solving these problems is using proximal gradient methods. To accelerate the convergence of…
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…
Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or…
Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel,…
In this paper we consider the problem of learning variational models in the context of supervised learning via risk minimization. Our goal is to provide a deeper understanding of the two approaches of learning of variational models via…
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…
When a facial image is blurred, it significantly affects high-level vision tasks such as face recognition. The purpose of facial image deblurring is to recover a clear image from a blurry input image, which can improve the recognition…
Single-Pixel Imaging (SPI) enables the reconstruction of objects using a single detector through sequential illuminations with structured light patterns. The choice of illumination patterns is critical, particularly in highly undersampled…
Image deblurring is a challenging problem in imaging due to its highly ill-posed nature. Deep learning models have shown great success in tackling this problem but the quest for the best image quality has brought their computational…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
We present a new approach for nonlocal image denoising, based around the application of an unnormalized extended Gaussian ANOVA kernel within a bilevel optimization algorithm. A critical bottleneck when solving such problems for…
This paper presents a multilevel FISTA algorithm, based on the use of the Moreau envelope to build the correction brought by the coarse models, which is easy to compute when the explicit form of the proximal operator of the considered…
The hyperparameter optimization of neural network can be expressed as a bilevel optimization problem. The bilevel optimization is used to automatically update the hyperparameter, and the gradient of the hyperparameter is the approximate…
Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…
Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes; yet, the observed images typically suffer from blur and background noise. In this work, we propose a…
In this paper, we consider the problem in defocus image deblurring. Previous classical methods follow two-steps approaches, i.e., first defocus map estimation and then the non-blind deblurring. In the era of deep learning, some researchers…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we…
Deep learning based single image super-resolution models have been widely studied and superb results are achieved in upscaling low-resolution images with fixed scale factor and downscaling degradation kernel. To improve real world…