Hadamard transform

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

Chemical Mapping in the Mid- and Near-IR Spectral Regions by Hadamard Transform/FT-IR Spectrometry

Abstract: A movable two-dimensional (2D) Hadamard encoding mask is obtained and combined with conventional FT-IR spectrometers for use in both the mid- and near-infrared spectral regions. Chemical maps and spectra of individual pixels of the maps can be obtained from heterogeneous samples by using this combination of a moveable 2D Hadamard encoding mask and an FT-IR spectrometer. We call the procedure Hadamard transform/FT-IR spectrometry. Spectra of usable signal-to-noise ratio and reliable chemical maps are obtained in reasonable data acquisition and processing time.

Thwarting Adversarial Examples: An $L_0$-Robust Sparse Fourier Transform

Abstract: We give a new algorithm for approximating the Discrete Fourier transform of an approximately sparse signal that is robust to worst-case $L_0$ corruptions, namely that some coordinates of the signal can be corrupt arbitrarily Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs We use our algorithm to successfully defend against worst-case $L_0$ adversaries in the setting of image classification We give experimental results on the Jacobian-based Saliency Map Attack (JSMA) and the CW $L_0$ attack on the MNIST and Fashion-MNIST datasets as well as the Adversarial Patch on the ImageNet dataset

Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations

Abstract: This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence of existence is obtained employing the alternative of Leray-Schauder, and Krasnoselskii's, whereas the uniqueness result, is based on the principle of Banach contraction mapping. We examine the stability of the solutions involved in the Hyers-Ulam type. A few examples are presented as an application to illustrate the main results. Finally, it addresses some variants of the problem.

Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag–Leffler functions

Abstract: In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral ...