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 Hadamard transformation was used to construct a transition matrix on probability amplitude and gave some results on symmetry of probability distributions for a one-dimensional quantum random walk.
Abstract: In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.
32 citations
TL;DR: Integration of holograms into multimode waveguides allows the implementation of arbitrary unitary mode transformations and unitary matrix-vector multiplication.
Abstract: Integration of holograms into multimode waveguides allows the implementation of arbitrary unitary mode transformations and unitary matrix-vector multiplication. Theoretical analysis is used to justify a design approach to implement specific functions in these devices. Based on this approach, a compact mode-order converter, a Hadamard transformer, and a spatial pattern generator-correlator are proposed and analyzed. Beam propagation simulations are used to verify the theoretical calculations and to address bandwidth, scalability, and fabrication criteria. Optical pattern generators were successfully fabricated using standard photolithographic techniques to demonstrate the feasibility of the devices.
32 citations
13 Jun 2010
TL;DR: Wang et al. as discussed by the authors proposed to use the orthogonal Haar transform (OHT) for pattern matching, the algorithm using strip sum requires O(log u) additions per pixel to project input data of size N × N onto u 2-D OHT basis.
Abstract: Pattern matching is a widely used procedure in signal processing, computer vision, image and video processing. Recently, methods using Walsh Hadamard Transform (WHT) and Gray-Code kernels (GCK) are successfully applied for fast transform domain pattern matching. This paper introduces strip sum on the image. The sum of pixels in a rectangle can be computed by one addition using the strip sum. Then we propose to use the orthogonal Haar transform (OHT) for pattern matching. Applied for pattern matching, the algorithm using strip sum requires O(log u) additions per pixel to project input data of size N × N onto u 2-D OHT basis while existing fast algorithms require O(u) additions per pixel to project the same data onto u 2-D WHT or GCK basis. Experimental results show the efficiency of pattern matching using OHT.
32 citations
TL;DR: In this paper, the class of -preinvex functions on the co-ordinates was introduced, and some new inequalities of Hermite-Hadamard and Fejer type for such mappings were proved.
Abstract: We introduce the class of -preinvex functions on the co-ordinates, and we prove some new inequalities of Hermite-Hadamard and Fejer type for such mappings. MSC:26A15, 26A51, 52A30.
32 citations
Patent•
30 Apr 1970TL;DR: In this article, the difference signal is distributed by transformation prior to coding, e.g., by quantizing, and transmission, preferably by means of the Fourier, Hadamard, or other unitary matrix transforms, to "'''scramble'' them relatively homogeneously in the domain of the transformed variable''.
Abstract: Immunity to transmission errors and worthwhile bandwidth reduction are achieved by distributing the difference signal, developed in differentially coding an image signal, over a spatially large interval or area, and transmitting the coded distributed signal instead of the image or differential signal. Line or frame image difference signals are, accordingly, dispersed by transformation prior to coding, e.g., by quantizing, and transmission, preferably by means of the Fourier, Hadamard, or other unitary matrix transforms, to ''''scramble'''' them relatively homogeneously in the domain of the transformed variable. Each transmitted image element thus represents a weighted sum of many or all of the elements of the corresponding line or frame. Simpler coding and other economies are achieved, particularly for relatively slowly varying sequences of images.
32 citations