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: The authors' analytic formulas provide a computationally efficient method for determining the performance of various coding schemes and show that for a uniform source and uniform quantizer, the natural binary code is never optimal for a nonsymmetric channel, even though it is known to be optimal forA symmetric channel.
Abstract: We determine analytic expressions for the performance of some low-complexity combined source-channel coding systems. The main tool used is the Hadamard transform. In particular, we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments, linear block channel coding, and a binary-symmetric channel. The distortion formulas are specialized to nonredundant channel codes for a binary-symmetric channel, and then extended to affine index assignments on a binary-asymmetric channel. Various structured index assignments are compared. Our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes. One interesting result shown is that for a uniform source and uniform quantizer, the natural binary code is never optimal for a nonsymmetric channel, even though it is known to be optimal for a symmetric channel.
38 citations
TL;DR: In this article, the authors obtained a sufficient and necessary condition for an analytic function f on D with Hadamard gaps, that is, for satisfying nk+1/nk ≥ λ 1 for all k, to belong to a kind of space consisting of analytic functions on D. The special cases of these spaces are BMOA and VMOA.
Abstract: In this paper we obtain a sufficient and necessary condition for an analytic function f on D with Hadamard gaps, that is, for satisfying nk+1/nk ≥ λ 1 for all k, to belong to a kind of space consisting of analytic functions on D. The special cases of these spaces are BMOA and VMOA. In view of our result we can answer the open question given recently by Stroethoff.
38 citations
TL;DR: In this paper, the authors show that H-matrix encoding results in no effect on average on the noise level due to Poisson noise sources while preferentially reducing additive noise.
Abstract: Hadamard multiplexing provides a considerable SNR boost over additive random noise but Poisson noise such as photon noise reduces the boost. We develop the theory for full H-matrix Hadamard transform imaging under additive and Poisson noise effects. We show that H-matrix encoding results in no effect on average on the noise level due to Poisson noise sources while preferentially reducing additive noise. We use this result to explain the wavelength-dependent varying SNR boost in a Hadamard hyperspectral imager and argue that such a preferential boost is useful when the main noise source is indeterminant or varying.
38 citations
01 Dec 2001
TL;DR: In this paper, the authors describe two approaches suitable for a field-programmable gate-array (FPGA) implementation of fast Walsh-Hadamard transforms using both a systolic architecture and distributed arithmetic techniques.
Abstract: The paper describes two approaches suitable for a field-programmable gate-array (FPGA) implementation of fast Walsh-Hadamard transforms. These transforms are important in many signal-processing applications including speech compression, filtering and coding. Two novel architectures for the fast Hadamard transforms using both a systolic architecture and distributed arithmetic techniques are presented. The first approach uses the Baugh-Wooley multiplication algorithm for a systolic architecture implementation. The second approach is based on both a distributed arithmetic ROM and accumulator structure, and a sparse matrix-factorisation technique. Implementations of the algorithms on a Xilinx FPGA board are described. The distributed arithmetic approach exhibits better performances when compared with the systolic architecture approach.
38 citations
TL;DR: An “Illumination Watermarking” technology with which the images of objects without copyright protection can contain invisible digital watermarking is proposed, and embedded data could be read out with almost 100% accuracy in both cases.
Abstract: We have proposed an “Illumination Watermarking” technology with which the images of objects without copyright protection can contain invisible digital watermarking. This technology uses spatially modulated illumination possibly using an orthogonal transform, such as discrete cosine transform (DCT), as the method of embedding watermarks, and it can be applied to objects that do not have electronically embedded watermarking such as pictures painted by artists. We conducted a new series of experiments where one-bit binary data were embedded in one block that consisted of 8 × 8 pixels using the phase of the highest frequency component generated by a Walsh-Hadamard transform (WHT) as well as DCT. The experimental results revealed that embedded data could be read out with almost 100% accuracy in both cases, where the embedded watermarked image could hardly be observed. We also found that the influence of JPEG compression, which is commonly used in digital cameras, was very small.
38 citations