Related papers: Variable Projection Methods for Solving Regularize…
We consider the problem of finding the best approximation point from a polyhedral set, and its applications, in particular to solving large-scale linear programs. The classical projection problem has many various and many applications. We…
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
We show that the sparse polynomial interpolation problem reduces to a discrete super-resolution problem on the $n$-dimensional torus. Therefore the semidefinite programming approach initiated by Cand\`es \\& Fernandez-Granda…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
Many computational problems involve solving a linear system of equations, although only a subset of the entries of the solution are needed. In inverse problems, where the goal is to estimate unknown parameters from indirect noisy…
In this paper we investigate the use of half-precision Kronecker product singular value decomposition (SVD) approximations as preconditioners for large-scale Tikhonov regularized least squares problems. Half precision reduces storage…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
We consider the problem of finding for a given $N$-tuple of polynomials (real or complex) the closest $N$-tuple that has a common divisor of degree at least $d$. Extended weighted Euclidean seminorm of the coefficients is used as a measure…
Variable thickness topology optimization (VTTO) is a potent methodology for designing high-performance, high-stiffness sheet structures. However, this method frequently encounters two primary challenges: 1) the formation of undesirable…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent…
Contrastive learning has proven to be highly efficient and adaptable in shaping representation spaces across diverse modalities by pulling similar samples together and pushing dissimilar ones apart. However, two key limitations persist: (1)…