Related papers: CPGD: Cadzow Plug-and-Play Gradient Descent for Ge…
The finite-rate-of-innovation (FRI) framework which corresponds a signal/image to a structured low-rank matrix is emerging as an alternative to the traditional sparse regularization. This is because such an off-the-grid approach is able to…
Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based…
High cost of training time caused by multi-step adversarial example generation is a major challenge in adversarial training. Previous methods try to reduce the computational burden of adversarial training using single-step adversarial…
A standard model for image reconstruction involves the minimization of a data-fidelity term along with a regularizer, where the optimization is performed using proximal algorithms such as ISTA and ADMM. In plug-and-play (PnP)…
We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step…
Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem.…
A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…
Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…
We study the proximal gradient descent (PGD) method for $\ell^{0}$ sparse approximation problem as well as its accelerated optimization with randomized algorithms in this paper. We first offer theoretical analysis of PGD showing the bounded…
Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the…
Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
Greedy point insertion algorithms have emerged as an attractive tool for the solution of minimization problems over the space of Radon measures. Conceptually, these methods can be split into two phases: first, the computation of a new…
Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
Sign Gradient Descent (SignGD) is a simple yet robust optimization method, widely used in machine learning for its resilience to gradient noise and compatibility with low-precision computations. While its empirical performance is well…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
The Cadzow's algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast Cadzow's algorithm which is developed by incorporating a…
Rectified-Flow (RF)-based generative models have recently emerged as strong alternatives to traditional diffusion models, demonstrating state-of-the-art performance across various tasks. By learning a continuous velocity field that…
In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with…