Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

Polynomial approximation via compressed sensing of high-dimensional functions on lower sets

Abstract: This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly decaying orthonormal expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we present an innovative weighted $\ell_1$ minimization procedure with a precise choice of weights, and a new iterative hard thresholding method, for imposing the downward closed preference. Theoretical results reveal that our computational approaches possess a provably reduced sample complexity compared to existing compressed sensing techniques presented in the literature. In addition, the recovery of the corresponding best approximation using these methods is established through an improved bound for the restricted isometry property. Our analysis represents an extension of the approach for Hadamard matrices in [5] to the general case of continuous bounded orthonormal systems, quantifies the dependence of sample complexity on the successful recovery probability, and provides an estimate on the number of measurements with explicit constants. Numerical examples are provided to support the theoretical results and demonstrate the computational efficiency of the novel weighted $\ell_1$ minimization strategy.

Two-timescale simultaneous perturbation stochastic approximation using deterministic perturbation sequences

Abstract: Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulation output performance measures at only two settings of the N-dimensional parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual one-sided or symmetric difference estimates, respectively. The two settings of the parameter vector are obtained by simultaneously changing the parameter vector in each component direction using random perturbations. In this article, in order to enhance the convergence of these algorithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms. Two constructions for the perturbation sequences are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation versions of SPSA have been proposed, and we also investigate these algorithms using deterministic sequences. Rigorous convergence analyses for all proposed algorithms are presented in detail. Extensive numerical experiments on a network of M/G/1 queues with feedback indicate that the deterministic sequence SPSA algorithms perform significantly better than the corresponding randomized algorithms.

Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions

Abstract: The authors introduce the concepts of m-invex set, generalized (s,m)-preinvex function, and explicitly (s,m)-preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized (s,m)-preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results. c ©2016 All rights reserved.

Hadamard Transform Time-of-Flight Mass Spectrometry

Abstract: A new mode of operation of a time-of-flight mass spectrometer (TOFMS) is described and demonstrated. A continuous ion beam emerging from the ion source is accelerated and then modulated by a pseudorandom sequence of “on” and “off” pulses. The data acquisition period is set to match the period of the modulation sequence, and data are acquired synchronously with the modulation of the ion beam. The modulation sequence is deconvoluted from the data using a fast Hadamard transform (FHT) algorithm to extract the time-of-flight distribution of the ions. This multiplexing scheme increases the ion usage to ∼50% for a single detector instrument and ∼100% for a multiple detector instrument, which improves the signal level considerably over that of conventional TOFMS. The gains in signal lead to an improved signal-to-noise ratio or alternatively reduced data acquisition time, giving HT-TOFMS a major instrumental advantage over conventional TOFMS in a number of applications at little additional cost. Positive mode ele...

Inequalities of Hermite-Hadamard Type for h-Convex Functions on Linear Spaces

Abstract: Some inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well.