Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: In this paper, the authors used the digital micro-mirror array (DMA) as a 2D Hadamard encoding mask for Raman hyper-spectral imaging in the visible spectral region.
28 citations
11 Feb 2009
TL;DR: In this article, the authors extend the Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system, which is the case in this paper.
Abstract: The aim of the present paper is to extend the classical Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system.
28 citations
TL;DR: The Hadamard transform Raman microscope equipped with a two-dimensional video detector is inherently capable of obtaining images at several different Raman frequencies simultaneously as mentioned in this paper, and the necessary software to exploit this multispectral capability is described in this communication.
Abstract: The Hadamard transform Raman microscope equipped with a two-dimensional video detector is inherently capable of obtaining images at several different Raman frequencies simultaneously. In this communication, we describe the necessary software to exploit this multispectral capability. We apply multispectral imaging to polymer laminates and to removal of artifacts from Raman images.
28 citations
TL;DR: One-dimensional and two-dimensional fast algorithms for realizing the center weighted Hadamard transform (CWHT) based on the Kronecker product and direct sum operations require fewer computations than the existing methods.
Abstract: In this paper, one-dimensional (1-D) and two-dimensional (2-D) fast algorithms for realizing the center weighted Hadamard transform (CWHT) are proposed. Based on the Kronecker product and direct sum operations, the proposed 1-D and 2-D CWHT algorithms through matrix decompositions require fewer computations than the existing methods. With low complexity and regular modularity, the proposed algorithms are suitable for VLSI implementation to achieve real-time signal processing and compression.
28 citations
TL;DR: In this article, the algebraic structure of linearly recursive sequences under the Hadamard product was described and the invertible elements and zero divisors were characterized using Hopf algebras.
Abstract: We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.
28 citations