Related papers: Bilevel learning of regularization models and thei…
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…
Low-rank adaptation (LoRA) is a popular method for fine-tuning large-scale pre-trained models in downstream tasks by learning low-rank incremental matrices. Though LoRA and its variants effectively reduce the number of trainable parameters…
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…
In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an…
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…
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…
Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
Image rescaling is a commonly used bidirectional operation, which first downscales high-resolution images to fit various display screens or to be storage- and bandwidth-friendly, and afterward upscales the corresponding low-resolution…
In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired…
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…
Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…
Most existing methods usually formulate the non-blind deconvolution problem into a maximum-a-posteriori framework and address it by manually designing kinds of regularization terms and data terms of the latent clear images. However,…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…
Blind image deblurring is an important yet very challenging problem in low-level vision. Traditional optimization based methods generally formulate this task as a maximum-a-posteriori estimation or variational inference problem, whose…
Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the output of…
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…