Showing papers on "Hadamard transform published in 1991"
TL;DR: It is shown that m-transforms are in the same Hadamard equivalence class as Walsh–Hadamard transforms and can be becomputed by means of the Fast Walsh Transform (FWT) algorithm, preceded and followed by a permutation.
Abstract: An algorithm is presented for the fast computation of the m-transform, a Hadamard transform intimately related to cross-correlation of analog signals with binary m-sequences. It is shown that m-transforms are in the same Hadamard equivalence class as Walsh–Hadamard transforms and can, thus, becomputed by means of the Fast Walsh Transform (FWT) algorithm, preceded and followed by a permutation. The FWT is performed in place in the original data array, while the permutations are executed during loading and reading of this array. Real-time generation of the array addresses for loading and reading adds little to execution time of the FWT. The implementation described here lends itself particularly well to applications in linear and nonlinear systems analysis.
228 citations
TL;DR: A technique for the simultaneous acquisition of three‐dimensional phase‐contrast angiograms and stationary‐tissue images is described and hadamard multiplexed encoding of flow information permits image acquisition times that are a third shorter than those of previous phase-contrast methods.
Abstract: A technique for the simultaneous acquisition of three-dimensional phase-contrast angiograms and stationary-tissue images is described. Hadamard multiplexed encoding of flow information permits image acquisition times that are a third shorter than those of previous phase-contrast methods. The encoding scheme described also enables differentiation of flow-induced phase shifts from phase shifts due to resonance offset conditions such as field inhomogeneities and chemical shift. Display strategies that combine this phase information with the flow image are described.
81 citations
TL;DR: In this paper, an algorithm that combines coarse discretization for inverting the Laplace transform with a nonlinear least-squares approach based on Newton and quasi-Newton techniques for solving the convolution equation was proposed.
51 citations
Patent•
25 Jul 1991TL;DR: A processor for generating a Walsh transform by substantially simultaneously calculating M combinations of M input values, wherein M=2N and the input values are two's-complement binary values, has N stages electrically connected in sequence, wherein each stage has a crisscross network of M conductors electrically connecting in a predetermined pattern to a set of M/2 butterflies, the butterflies having devices for calculating sums and differences of respective values presented by their respective criss-cross networks.
Abstract: A processor for generating a Walsh transform by substantially simultaneously calculating M combinations of M input values, wherein M=2N and the input values are two's-complement binary values, has N stages electrically connected in sequence, wherein each stage has a criss-cross network of M conductors electrically connected in a predetermined pattern to a set of M/2 butterflies, the butterflies having devices for calculating sums and differences of respective values presented by their respective criss-cross networks and presenting the sums and differences to respective conductors of the next stage's criss-cross network. The input values are presented to the criss-cross network of the first stage serially and least-significant-bit first, and substantially synchronously therewith, the Walsh transform of the input values is serially produced by the butterflies of the N-th stage.
37 citations
TL;DR: In this article, a B1-insensitive Hadamard spectroscopic imaging technique for multivolume localization is presented and tested experimentally, which is achieved by using RF pulses which invert spins adiabatically at several well defined slices simultaneously.
31 citations
Patent•
IBM1
TL;DR: In this article, a technique for robustness against burst (or similar) errors to data patterns, such as illustratively two-dimensional image data, that exhibit local redundancy is proposed.
Abstract: A technique for use in, illustratively, a transform coder for imparting robustness against burst (or similar) errors to data patterns, such as illustratively two-dimensional image data, that exhibit local redundancy. Robustness is provided, in the case of images, by passing localized (blocked) image data, i.e. either pixel values or transformed, illustratively discrete cosine transform (DCT), image coefficient values therefor, through a global block transform, such as a global block Hadamard transform, prior to compression coding in order to produce "holographic-like" compressed data for subsequent transmission and/or storage. Specifically, globally transforming an image in this fashion effectively spreads (diffuses) the image data in each block of pixels in that image or in the transform coefficients therefor in a regularly ordered pre-defined global manner throughout the entire image to create what is, in effect, intentionally "smeared" image data. By subjecting the "smeared" image data upon de-compression to an inverse global block transformation, such as an inverse global block Hadamard transformation, then, even if a portion of the "smeared" data for an image is obliterated during transmission or playback, the entire image can still be advantageously reconstituted, though at a somewhat degraded quality, from the remaining "smeared" data.
30 citations
TL;DR: In this paper, it was shown that the number of equivalence classes of inverse orthogonality matrices in non-prime order and in order ≤ 3 is the same as that of unit Hadamard matrices.
Abstract: In 1867, Sylvester considered n × n matrices, (aij), with nonzero complex-valued entries, which satisfy (aij)(aij−1) = nI Such a matrix he called inverse orthogonal. If an inverse orthogonal matrix has all entries on the unit circle, it is a unit Hadamard matrix, and we have orthogonality in the usual sense. Any two inverse orthogonal (respectively, unit Hadamard) matrices are equivalent if one can be transformed into the other by a series of operations involving permutation of the rows and columns and multiplication of all the entries in any given row or column by a complex number (respectively a number on the unit circle). He stated without proof that there is exactly one equivalence class of inverse orthogonal matrices (and hence also of unit Hadamard matrices) in prime orders and that in general the number of equivalence classes is equal to the number of distinct factorisations of the order. In 1893 Hadamard showed this assertion to be false in the case of unit Hadamard matrices of non-prime order. We give the correct number of equivalence classes for each non-prime order, and orders ≤ 3, giving a complete, irredundant set of class representatives in each order ≤ 4 for both types of matrices.
29 citations
TL;DR: The Hadamard transform Raman microscope equipped with a two-dimensional video detector is inherently capable of obtaining images at several different Raman frequencies simultaneously as mentioned in this paper, and the necessary software to exploit this multispectral capability is described in this communication.
Abstract: The Hadamard transform Raman microscope equipped with a two-dimensional video detector is inherently capable of obtaining images at several different Raman frequencies simultaneously. In this communication, we describe the necessary software to exploit this multispectral capability. We apply multispectral imaging to polymer laminates and to removal of artifacts from Raman images.
28 citations
TL;DR: Hadamard transform spectrometry (HTS) provides a means of obtaining a multiplex advantage with a dispersive spectrometric technique Two recent advances, stationary electro-optic encoding masks and efficient spectrum-recovery techniques to compensate for nonidealities in the masks, have combined to revive interest in HTS as mentioned in this paper.
25 citations
TL;DR: The source coding scheme for the experimental research prototype that is currently being designed to demonstrate the digital coding of high-definition television (HDTV) for transport within the proposed broadband integrated services digital network (ISDN) fiber optic network is described.
Abstract: The source coding scheme for the experimental research prototype that is currently being designed to demonstrate the digital coding of high-definition television (HDTV) for transport within the proposed broadband integrated services digital network (ISDN) fiber optic network is described. The network interface will be used on a packet-based asynchronous transfer mode (ATM) technology. To maximize coding efficiency, run-length coding and variable word length coding are also incorporated in the system. The scheme uses multiple block-size Hadamard transform coding that can be implemented using a set of two-tap filters in a simple subband structure. In spite of the low hardware complexity, which is of dominant importance in the overall system performance, high coding efficiency is obtained. The major features and advantages of this scheme are outlined. >
Journal Article•
TL;DR: It has been shown as mentioned in this paper that the remainder term of a form of the Taylor expansion, involving Hadamard derivative, of the statistical functional is asymptotically negligible, and this result is extended to a more general form with respect to weighted empirical processes in order to establish some (uniform) linear functional approximations, which is usually needed for drawing statistical conclusions.
Patent•
12 Jul 1991
TL;DR: In this article, the average mean square error was reduced by a factor of 4N/(1+N) 2, where N is the number of points in the optical time domain reflectometry system.
Abstract: An optical time domain reflectometry method and apparatus that employs Hadamard transforms to increase the signal-to-noise ratio. A sequence of N pulses of light corresponding to a Hadamard derived code are launched down a fiber optic cable for each of N such codes. Selected combinations of pulses of reflected light are transformed by a Hadamard derived matrix to a set of equations that are solved simultaneously to determine the power reflected from each of N points. Where a Hadamard code is used the average mean square error is reduced by a factor of 1/N. Where a simplex code is employed the average mean square error is reduced by a factor of 4N/(1+N) 2 . In addition, N measurements of the power reflected at each point are computed and averaged.
TL;DR: In this paper, a 255 element polymer-dispersed liquid-crystal (PDLC) optical-shutter-array was used as a stationary Hadamard encoding mask.
01 Jan 1991
TL;DR: It is proved that if there exist Hadamard matrices of order h and n divisible by 4 then there exist two disjoint W(1/4hn, 1/8hn), whose sum is a (1, -1) matrix and a complex Hadamards matrix of order 1/ 4hn.
Abstract: We prove that if there exist Hadamard matrices of order h and n divisible by 4 then there exist two disjoint W(1/4hn, 1/8hn), whose sum is a (1, -1) matrix and a complex Hadamard matrix of order 1/4hn, furthermore, if there exists an OD(m; s1, s2,··· ,sl) for even m then there exists an OD(1/4hnm; 1/4hns1, 1/4hns2,···, 1/4hnsl). Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry and Xian-Mo Zhang, Some orthogonal designs and complex Hadamard matrices by using two Hadamard matrices, Australasian Journal of Combinatorics, 4, (1991), 93-102. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1057
01 Jan 1991
TL;DR: Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k2 whenever complete regular 4-sets of regular matrices of order k2 exist.
Abstract: It is shown that SBIED( 4k 2 , 2Jc 2 ± k, P ± k) and Hadamard matrices with maximal excess exist for qs,q {q:q 1 (mod 4) is a prime power}, sE {1, ... ,33,37, ... ,41,45, ... ,59} U + 1, g the length of a Golay sequence}. This the following odd k < 250 undecided 47,71,77,79, lO3,107,127, 131,133,139, 141,151,163,167,177,179,191,199,209, ... ,217,223,227, 231,233,237,239,243,249. There a proper n dimensional Hadamard matrix of order (4k2)n. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k2 whenever complete regular 4-sets of regular matrices of order k2 exist.
TL;DR: It is shown that if there is a skew-Hadamard matrix of order m then there is an Hadamard matrices of order 4m2−4m whose excess attains the maximum possible bound predicted by S. Kounias and N. Farmakis.
TL;DR: In this paper, a Hadamard approach employing an encoding mask at the entrance to a spectrograph and a multichannel detector is described for a variety of emission-mode measurements requiring collection of radiation from an extended source.
Abstract: A Hadamard approach employing an encoding mask at the entrance to a spectrograph and a multichannel detector is described. This approach provides an energy throughput advantage which should prove important for a variety of emission-mode measurements requiring collection of radiation from an extended source. The performance of the system is demonstrated for mercury lamp atomic emission and rhodamine B fluorescence measurements. Simulations are used to investigate mechanical requirements in the construction of the system.
TL;DR: A novel directionally classified subspace image vector quantisation coding scheme using a new gradient based edge classifier and Walsh Hadamard transform subspace distortion measures is proposed to reduce both the computational complexity and memory requirement of the conventional classified vectors quantisation technique.
Abstract: A novel directionally classified subspace image vector quantisation coding scheme using a new gradient based edge classifier and Walsh Hadamard transform subspace distortion measures is proposed. The new coding scheme can reduce both the computational complexity and memory requirement of the conventional classified vector quantisation technique3 while the reproduced image quality is maintained.
01 Jan 1991
TL;DR: In this article, the authors provided an overview of symmetric Hadamard matrices of order 36 and showed that these matrices are nonequivalent with respect to switching, with one exceptional pair.
Abstract: Publisher Summary
This chapter provides an overview of symmetric Hadamard matrix of order 36. A square matrix H is a Hadamard matrix if its elements are + 1 and if it is orthogonal. If in addition, H is symmetric, has a constant diagonal I, and has order 36, then H2 = 36I, H = HT, H = A + I, (A−5I) (A+7I) = 0.The chapter explains a method to obtain symmetric Hadamard matrices of order 36 from the 12 Latin squares of order 6, and from the 80 Steiner triple systems of order 15 . The graphs obtained in this way are shown to be nonequivalent with respect to switching, with one exceptional pair. The method consists of counting void and complete sub-graphs, and is capable of wider application. The chapter also explains how graphs of the Steiner type can be switched into strongly regular graphs. Among these graphs, there are 23 that can be made regular with valency 21, whereas all 80 can be made regular with valency I5. This follows from a computer search by which each of the 80 Steiner triple systems appears to contain a 3-factor, that is, a subsystem of 15 triples in which every symbol occurs exactly three times.
TL;DR: It is noted that under certain circumstances, quadtree compression produces identical results to Walsh transform coding, but requires less computational effort to do so.
Abstract: Transforms and quadtrees are both methods of representing information in an
image in terms of the presence of information at differing length scales This paper
presents a mathematical relationship between these two approaches to describing
images in the particular case when Walsh transforms are used Furthermore, both
methods have been used for the compression of images for transmission This paper
notes that under certain circumstances, quadtree compression produces identical
results to Walsh transform coding, but requires less computational effort to do so
Remarks are also made about the differences between these approaches
TL;DR: Another proof of Kharaghani's result is given, by generalizing an example of Farmakis and Kounias, that the maximal excess of the bound is attained if m ≡ 2 (mod 4) is the order of a conference matrix.
TL;DR: In this paper, it was shown that any m×n±1 matrix may be embedded in a Hadamard matrix of order kl, where k and l are the least orders greater than or equal to m and nrespectively in which hadamard matrices exist.
Abstract: It is shown that any m×n±1 matrix may be embedded in a Hadamard matrix of order kl, where k and l are the least orders greater than or equal to m and nrespectively in which Hadamard matrices exist.
TL;DR: A set of new order-16 integer transforms is found and the kernel components of the new integer transforms can be represented by one-byte integers, which have better performance and basis restriction mean-square-error than the discrete cosine transform.
TL;DR: Two contributions are made to the implementation of fast discrete cosine transform algorithms by using Hadamard ordering to improve the regularity of the Lee fast cosine transforms and derives a close relationship between the Lee FCT and the recursive algorithm for the DCT.
Abstract: Two contributions are made to the implementation of fast discrete cosine transform algorithms. The first uses Hadamard ordering to improve the regularity of the Lee fast cosine transform (FCT) algorithm for the discrete cosine transform (DCT). The second derives a close relationship between the Lee FCT and the recursive algorithm for the DCT.
01 Jun 1991
TL;DR: This paper introduces a new class of artificial neural network (ANN) models based on transformed domain feature extraction, using the FT and WHT domain features and has used these ANN models for invariant object recognition.
Abstract: In this paper we introduce a new class of artificial neural network (ANN) models based on transformed domain feature extraction. Many optical and/or digital recognition systems based on transformed domain feature extraction are available in practice. Optical systems are inherently parallel in nature and are preferred for real time applications, whereas digital systems are more suitable for nonlinear operations. In our ANN models we combine advantages of both digital and optical systems. Many transformed domain feature extraction techniques have been developed during the last three decades. They include: the Fourier transform (FT), the Walsh Hadamard transform (WHT), the discrete cosine transform (DCT), etc. As an example, we have developed ANN models using the FT and WHT domain features. The models consist of two stages, the feature extraction stage and the recognition stage. We have used back-propagation and competitive learning algorithms in the recognition stage. We have used these ANN models for invariant object recognition. The models have been used successfully to recognize various types of aircraft, and also have been tested with test patterns. ANN models based on other transforms can be developed in a similar fashion.