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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, a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π:A_s(n) to B(H) was developed.
Abstract: We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type $\pi:A_s(n)\to B(H)$. We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can be performed up to $n=6$.
25 citations
TL;DR: C cubature formulas based on bivariate C1 local polynomial splines with a four directional mesh with Hadamard finite part sense are generated and studied and Computational features, convergence properties and error bounds are proved.
Abstract: In this paper cubature formulas based on bivariate C1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.
25 citations
TL;DR: A new reversible watermarking scheme based on error prediction in Hadamard domain is presented and it is shown that the proposed method provides higher capacity and quality in comparison to some well-known methods.
Abstract: Reversible watermarking is a special kind of the lossless data hiding techniques which allows lossless recovering of both the watermark and the host image. In this paper, a new reversible watermarking scheme based on error prediction in Hadamard domain is presented. In the proposed method, the original image is divided into blocks and transformed to Hadamard domain. If a block is in a smooth area, its AC coefficients will be predicted using a linear predictor function. Then the value of error between the original and the predicted coefficient is computed. At last, a watermark bit will be embedded in the error. To reduce the error value, an Adaline neural network is used to determine coefficients of the predictor function. The experimental results show that the proposed method provides higher capacity and quality in comparison to some well-known methods.
25 citations
Patent•
05 Aug 1981TL;DR: In this paper, a buffer memory with the capacity equal to the number of components of an input vector to be transformed is provided and addressed in such a way computation of Hadamard transforms can be performed at faster speeds with a higher degree of efficiency.
Abstract: Devices for performing fast Hadamard transforms based upon a predetermined algorithm are provided. A buffer memory (random-access memory) with the capacity equal to the number of components of an input vector to be transformed is provided and is addressed in such a way computation of Hadamard transforms can be performed at faster speeds with a higher degree of efficiency.
24 citations
TL;DR: In this paper, an important computation rule for tangent cones is examined and two results are given which assume only Hadamard differentiability (and a variant of it) instead of strict Frechet differentiability.
Abstract: An important computation rule for tangent cones is examined. Two results are given which assume only Hadamard differentiability (and a variant of it) instead of strict Frechet differentiability. This allows the consideration of concrete examples such as superposition operators and can be applied to the problem of linearizing a nonlinear equation or inequality.
24 citations