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We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…
The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…
It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
Distributed renewable generation, elastic loads, and purposeful manipulation of meter readings challenge the monitoring and control of today's power systems (PS). In this context, to maintain a comprehensive view of the system in real time,…
Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift.…
In the realm of image processing and computer vision (CV), machine learning (ML) architectures are widely applied. Convolutional neural networks (CNNs) solve a wide range of image processing issues and can solve image compression problem.…
Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Modern digital cameras rely on the sequential execution of separate image processing steps to produce realistic images. The first two steps are usually related to denoising and demosaicking where the former aims to reduce noise from the…
In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
Quantum compressed sensing is the fundamental tool for low-rank density matrix tomographic reconstruction in the informationally incomplete case. We examine situations where the acquired information is not enough to allow one to obtain a…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly…
This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…
Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…