Hadamard transform

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

Biunitary constructions in quantum information

Abstract: We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary connections, algebraic objects which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method.

Performance analysis of hardware oriented algorithm modifications in H.264

Abstract: H.264 [Committee Draft of Joint Video Specification, July 2002] is initiated by ITU-T as H.26L and will become a joint standard of ITU-T and MPEG. The coding complexity of H.264 is much higher than MPEG-4 simple profile and advance simple profile algorithms. In order to achieve real-time encoding, hardware implementation is required. The original test model of H.264 (JM) [Joint Video Team, August 2002] is designed to achieve high coding performance. Some algorithms of the test model require lots of operations with little coding efficiency improvement. And some algorithms create data dependencies that prevent parallel hardware accelerations. This paper presents analysis of H.264 video coding algorithm in a hardware-oriented viewpoint. Intra prediction, Hadamard transform and motion estimation algorithms are reviewed and modified to a hardware friendly configuration. The rate distortion penalties of these modifications are simulated and shown in this paper.

Rank and kernel of binary Hadamard codes

Abstract: In this paper, the rank and the dimension of the kernel for (binary) Hadamard codes of length a power of two are studied. In general, it is well-known that the rank of a Hadamard code of length n=2/sup t/ is a value in {t+1,...,n/2}. In the present paper, the range of possible values for the dimension of the kernel is computed and a construction of Hadamard codes of length n=2/sup t/ for each one of these values is given. Lower and upper bounds for the rank and dimension of the kernel of a Hadamard code of length n=2/sup t/ are also established. Finally, we construct Hadamard codes for all possible ranks and dimension of kernels between these bounds.

Certain Gronwall type inequalities associated with Riemann-Liouville k-and Hadamard k-fractional derivatives and their applications

Abstract: We aim to establish certain Gronwall type inequalities associated with Riemann-Liouville k-and Hadamard k-fractional derivatives. The results presented here are sure to be new and potentially useful, in particular, in analyzing dependence solutions of certain k-fractional differential equations of arbitrary real order with initial conditions. Some interesting special cases of our main results are also considered.

A Robust Watermarking Scheme Using Sequency-ordered Complex Hadamard Transform

Abstract: This paper presents a robust phase watermarking scheme for still digital images based on the sequency-ordered complex Hadamard transform (SCHT). The transform matrix of the SCHT exhibits sequency ordering which is analogous to frequency in the discrete Fourier transform (DFT). Hence, sequency-based image analysis can be performed for image watermarking while providing simple implementation and with less computational complexity for computation of the transform. As the SCHT coefficients are complex numbers which consist of both magnitudes and phases, they are suited to adopt phase modulation techniques to embed the watermark. In this proposed scheme, the phases of the SCHT coefficients in the sequency domain are altered to convey the watermark information using the phase shift keying (PSK) modulation. Low amplitude block selection (LABS) is used to enhance the imperceptibility of digital watermark, and amplitude boost (AB) method is employed to improve the robustness of the watermarking scheme. Spread spectrum (SS) technique is adopted to increase the security of watermark against various unintentional or intentional attacks. In order to demonstrate the effectiveness of the proposed watermarking scheme, simulations are conducted under various kinds of attacking operations. The results show that the proposed scheme is able to sustain a series of attacks including common geometric transformations such as scaling, rotating, cropping, painting, and common image-processing operations such as JPEG compression, low-pass filtering, sharpening, noising and phase perturbation, etc. Comparisons of the simulation results with the other schemes are also mentioned and the results reveal that the proposed scheme shows better robustness.