Related papers: A simple algorithm for uniform sampling on the sur…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials…
This paper presents a method to obtain geometric registrations between high-genus ($g\geq 1$) surfaces. Surface registration between simple surfaces, such as simply-connected open surfaces, has been well studied. However, very few works…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…
A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem.…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
Environment maps with high dynamic range lighting, such as daylight sky maps, require importance sampling to keep the balance between noise and number of samples per pixel manageable. Typically, importance sampling schemes for environment…
There are (at least) two reasons to study random polytopes. The first is to understand the combinatorics and geometry of random polytopes especially as compared to other classes of polytopes, and the second is to analyze average-case…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…
A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational…
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…