Related papers: Unified Convex Optimization Approach to Super-Reso…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…
An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…
In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…
Image superresolution involves the processing of an image sequence to generate a still image with higher resolution. Classical approaches, such as bayesian MAP methods, require iterative minimization procedures, with high computational…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
Locating the center of convex objects is important in both image processing and unsupervised machine learning/data clustering fields. The automated analysis of biological images uses both of these fields for locating cell nuclei and for…
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…
Unimodular sequences with good auto/cross-correlation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences. The main content is as follows: first, we…