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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01 Jan 2003
TL;DR: In this paper, the authors discuss algorithms for the construction of Hadamard matrices and give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.
Abstract: We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction.Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44.The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.
43 citations
01 Jan 2009
TL;DR: In this article, some inequalities of Hermite-Hadamard type for boolean functions whose derivatives absolute values are quasi-convex, and error estimates for the midpoint formula are also obtained.
Abstract: In this paper, some inequalities of Hermite-Hadamard type for
functions whose derivatives absolute values are quasi-convex, are given. Some
error estimates for the midpoint formula are also obtained.
43 citations
TL;DR: In this paper, nonsmooth variational inequality problem (NVIP) and minty NVIP in terms of a bifunction are considered in the setting of Hadamard manifolds.
Abstract: Nonsmooth variational inequality problem (NVIP) and Minty nonsmooth variational inequality problem (MNVIP) in terms of a bifunction are considered in the setting of Hadamard manifolds. We f...
43 citations
TL;DR: The matrices of APBT based on WT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT, and the quantization table is simplified and the transform coefficients can be quantized uniformly.
Abstract: This paper proposes new concepts of the all phase biorthogonal transform (APBT) and the dual biorthogonal basis vectors. In the light of all phase digital filtering theory, three kinds of all phase biorthogonal transforms based on the Walsh transform (WT), the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT) are proposed. The matrices of APBT based on WT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT. Compared with DCT-based JPEG (DCT-JPEG) image compression algorithm at the same bit rates, the PSNR and visual quality of the reconstructed images using these transforms are approximate to DCT, outgoing DCT-JPEG at low bit rates especially. But the advantage is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation easier.
43 citations
Posted Content•
TL;DR: In this article, the proximal point method for a special class of nonconvex functions on a Hadamard manifold is presented, and it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and its convergence for a minimizer is obtained.
Abstract: In this paper we present the proximal point method for a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.
42 citations