Related papers: Adaptive multipliers for extrapolation in frequenc…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
There are many problems in machine learning and data mining which are equivalent to selecting a non-redundant, high "quality" set of objects. Recommender systems, feature selection, and data summarization are among many applications of…
This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a…
We present an algorithm for the forward propagation of intervals through the discrete Fourier transform. The algorithm yields best-possible bounds when computing the amplitude of the Fourier transform for real and complex valued sequences.…
The exponential explosion of the set of patterns is one of the main challenges in pattern mining. This challenge is approached by introducing a constraint for pattern selection. One of the first constraints proposed in pattern mining is…
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a…
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…