Showing papers on "Hadamard transform published in 1988"
87 citations
TL;DR: In this article, the authors obtained explicit formulae for degrees on diagonals, Hadamard products and Lamperti products, and showed that they can be expressed as follows:
Abstract: We obtain explicit formulae for degrees on diagonals, Hadamard products and Lamperti products.
24 citations
TL;DR: Improved upper bounds are given for σ ( n ) and a procedure is described to find all row-sum or column-sum vectors of an Hadamard matrix with given excess.
23 citations
TL;DR: Even-odd transforms such as the discrete cosine (DCT), the discrete sine, the slant (ST), and the discrete Legendre (DLT) transforms are developed from the Walsh-Hadamard transform (WHT).
20 citations
TL;DR: Hadamard mask encoding as discussed by the authors allows medium to high spatial resolution imaging with unfocused laser beams, where a laser beam is imaged on the sample through a series of masks and the spatially encoded signals from each of n masks, each containing n resolution elements, are measured.
Abstract: Hadamard mask encoding allows medium to high spatial resolution imaging with unfocused laser beams. A laser beam is imaged on the sample through a series of masks. The spatially encoded signals from each of n masks, each containing n resolution elements, are measured. The spatial distribution of the signal is recovered by Hadamard transformation of the matrix of encoded signals. Of course, the laser could be focused to an area equal to the unit resolution element. But, encoding with n-element masks reduces the power density at any point on the sample by a factor of n. We have already successfully employed masks containing 28 − 1 elements, and have estimated that it is feasible to use masks with 210 − 1 or even 212 − 1 elements. Reducing laser power density by a factor of 103 broadens the scope of spatially resolved laser spectroscopy and opens the possibility of Raman microscopy with pulsed lasers.
18 citations
TL;DR: It is established that there are four non-equivalent Hadamard matrices of the Williamson type of order 4·33, and an algorithm is given reducing considerably the required computational time and suitable when m is not a prime.
18 citations
16 citations
TL;DR: In this article, the authors make some remarks in connection with the results of Secs. 6-10, Sec. 6, 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 34
Abstract: We make some remarks in connection with the results of Secs. 6–10.
1.
We have used expansions into orthogonal series. In the general case it is natural to use spectral expansions of linear selfadjoint operators. For this one may use the results of [13, 14].
2.
Can the concept of weak well-posedness be carried over to nonlinear problems? Here, probably, J. F. Colombeau's method will turn out to be useful (see [13, 14]).
10 citations
TL;DR: A new method based on spatial-temporal Hadamard transform is proposed to estimate the 3-D translational motion parameters, which has no restriction on the magnitude of displacement for an image of size 2 n × 2 n.
10 citations
TL;DR: The present authors provide additional information on the structure of G/sub w/ and generalize some results by C.J. Zarowski and M. Yunik (see ibid., vol.ASSP-33, p.1246-52, Oct. 1985).
Abstract: A.E. Kahveci and E.L. Hall (see IEEE Trans. Comput., vol.C-23, no.9, p.976-81, Sept. 1974) introduced the concept of filtering discrete Fourier transform (DFT) spectra in the Walsh sequency domain. This is accomplished by finding a real and block-diagonal Walsh filter matrix G/sub w/ in the Walsh domain that performs the sample filtering operation as the prototype complex diagonal Fourier filter matrix G/sub f/ in the Fourier domain. The present authors provide additional information on the structure of G/sub w/ and generalize some results by C.J. Zarowski and M. Yunik (see ibid., vol.ASSP-33, p.1246-52, Oct. 1985). They consider a more general class of transforms, the T transforms, and the structure of the resulting T transform filter matrices G/sub t/. Examples of T besides T=W are considered, such as the Harr transform and fourth-order Chrestenson transform. The implementation of the presented DFT spectrum filtering techniques using linear systolic arrays is briefly considered. >
9 citations
TL;DR: In this paper, the modulation transfer function of a source-encoded Hadamard transform imaging system including beam condensing optics is derived and the effects of diffraction, convolution with the encoding apertures, mask motion, and focus errors are considered explicitly.
Abstract: The modulation transfer function of a source-encoded Hadamard transform imaging system including beam condensing optics is derived. The effects of diffraction, convolution with the encoding apertures, mask motion, and focus errors are considered explicitly. The derived equations are shown to describe resolution of Hadamard transform photothermal deflection imagers with up to 30× condensing optics.
TL;DR: It is shown that the information content for different truncations varies in the same way for both transformations, while the execution of FHT is about 8 times faster than that of FFT.
TL;DR: A coherent optical system composed of a holographic mask and two Fourier lenses is described for performing an arbitrary linear transform that is optically made in 1-D space.
Abstract: A coherent optical system composed of a holographic mask and two Fourier lenses is described for performing an arbitrary linear transform. A set of equations for determining the amplitude-phase distribution of the mask is given. As a specific transform, the Walsh-Hadamard transform for orders 32 and 64 is optically made in 1-D space.
TL;DR: It is shown that the maximal excess of Hadamard matrices of order 22t is 23t, which was proved by J. Hammer, R. Levingston and J. Seberry [4].
Abstract: In this paper we give a new series of Hadamard matrices of order 2t. When the order is 16, Hadamard matrices obtained here belong to class II, class V or to class IV of Hall's classification [3]. By combining our matrices with the matrices belonging to class I, class II or class III obtained before, we can say that we have direct construction, namely without resorting to block designs, for all classes of Hadamard matrices of order 16.
21 Jan 1988
TL;DR: Mapping of a Fast Fourier Transform, Haar Transform and Hadamard Transform algorithms onto a small, two-dimensional, mesh-connected array of processors makes it possible to reduce significantly the number of memory locations needed for the constants.
Abstract: The paper discusses mapping of a Fast Fourier Transform (FFT), Haar Transform and Hadamard Transform algorithms onto a small, two-dimensional, mesh-connected array of processors. The FFT algorithm is an in-place, decimation in frequency, Cooley-Tuckey algorithm in radix 2 and radix 4 versions applied to multidimensional, complex inputs. The data flow of the algorithms has been implemented on the array using an efficient, regular data transfer pattern, uniform for all the algorithms. The inputs and constants used in the algorithms are prestored in the local memories of the processors. The mapping makes it possible to reduce significantly the number of memory locations needed for the constants. A partitioning scheme has been developed for the algorithms which allows us to execute them with inputs of arbitrary size on a small processor array. Also an algorithm has been proposed for the processor array, which efficiently unscrambles the bit reversed output of the FFT algorithm. The processors of the array have East, West, North, South interconnections with their nearest neighbors. The local memory of the processors is small, on the order of hundreds of locations. The processors are controlled in Single Instruction Multiple Data Stream (SIMD) mode and can be selectively disabled using simple masks, consisting of combinations of rows or columns.
TL;DR: In this article, the authors gave another proof of singular value inequality for any A B ∊Mn (C), which has been obtained recently in {1, 3, 4, 7].
Abstract: Let A B denote the Hadamard productb of A and B A B the same size complex matrices. let σ(A) denote the singular value vector of A. with components in decreasing order and let Mn (C) denote the space of all complex n×n matrices. This pater gives another proof of singular value inequality for any A B∊Mn (C), which has been obtained recently in {1, 3, 4, 7].
TL;DR: In this article, a supersymmetrically extended version of the Hadamard model is investigated, and the quantized energy sum rule is shown to be a superanalog of the Selberg trace formula.
01 Jan 1988
TL;DR: In this paper, the authors give a list for Hadamard matrices of order ≤ 1000 of the smallest upper bounds known for the excess for each order for the maximal known excess.
Abstract: We give some results on the excess of Hadamard matrices. We give a list for Hadamard matrices of order ≤1000 of the smallest upper bounds known for the excess for each order. A construction is indicated for the maximal known excess. Disciplines Physical Sciences and Mathematics Publication Details Jenkins, BA, Koukouvinos, C, Kounias, S, Seberry, J & Seberry, R, Some results on the excesses of Hadamard matrices, JCMCC, 4, 1988, 155-188. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1035 Some Results on the Excesses of Hadamard Matrices Brett A.Jenkins", C.KoukouvinQlt, S,Kouni4st, Jennifer Seberry·, Ralph Seberry*
19 Jan 1988
TL;DR: In this paper, the advantages and disadvantages of the Fourier transform spectroscopy (FTS) and the classical dispersive method are compared in the context of Raman Spectroscopy.
Abstract: Hadamard transform spectroscopy is showing signs of emerging again even though turf protectors would prefer that it remain benign. In this discussion, some of its advantages, and there are some, and some of its disadvantages, and there are some of those as well, are discussed. Competing approaches including the classical dispersive method and Fourier transform spectroscopy are included in the discussion especially where the comparisons are relevant to applications in Raman spectroscopy.
07 Jun 1988
TL;DR: In this paper, a switched-capacitor discrete Walsh transform circuit is proposed, which is improved in simplicity by using the proposed circuit, and this circuit has a speed advantage because of analog processing.
Abstract: A novel switched-capacitor discrete Walsh transform circuit is proposed. The Walsh hardware transformation is improved in simplicity by using the proposed circuit, and this circuit has a speed advantage because of analog processing. Furthermore, a switched-capacitor inverse Walsh transform circuit is constructed. A switched-capacitor sequence filter is also proposed which combines the Walsh transform circuit and its inverse. >
TL;DR: In this paper, the amplitude of a sinusoidal signal superimposed on a constant background can be determined from Hadamard sums, which corrects a quadratic nonlinearity in the signal detection.
Abstract: In a perfect system, the amplitude of a sinusoidal signal superimposed on a constant background can be determined from Hadamard sums. The simple computation described here allows us to correct a quadratic nonlinearity in the signal detection. Using this procedure, a commercial rotating‐polarizer ellipsometer could be safely operated with signal levels increased by a factor of 15.
TL;DR: In this article, a method for the construction of v × b matrices with elements 1, −1, such that XX′ = bI, is given, where bI is the number of elements in the matrix.
20 Mar 1988
TL;DR: In this paper, a four-level Hadamard transform is presented, which maintains the same row orthogonality as the binary hadamard transformation but requires the use of complex numbers.
Abstract: A four-level Hadamard transform that is more general than the binary Hadamard transform is presented. The transform maintains the same row orthogonality as the binary Hadamard transform but requires the use of complex numbers. A four-level Walsh transform is also obtained from the four-level Hadamard transform. These four-level transforms are applicable to image and speech processing. >
01 Aug 1988-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: It is shown in the paper that regularization problems, such as the smoothest velocity field computation and the computation of the minimum dilatation velocity field, can be solved with a parallel algorithm or a fast sequential algorithm.
Abstract: The computation of the velocity field along image curves belongs to the class of ill-posed problems (in the sense of Hadamard). Local measurements of image pattern changes are usually insufficient to solve the velocity field uniquely. Therefore regularization techniques are applied, yielding solutions that are robust against noise and that are correct for a limited class of curve velocity fields. It is shown in the paper that regularization problems, such as the smoothest velocity field computation and the computation of the minimum dilatation velocity field, can be solved with a parallel algorithm or a fast sequential algorithm. This follows from the block-tridiagonal structure to which these variational techniques give rise.
Patent•
05 Sep 1988
TL;DR: In this article, the Hadamard inverse transform circuit was used to simplify a device constitution by constituting a parallel/serial conversion circuit used for parallel and serial conversion in such a way that a part of picture element data among parallel picture elements obtained from HadamARD inverse transform is substituted for other picture elements data, whereby only the output of data x'13 instead of them may be enough in a period when original data x''-x'13 are outputted.
Abstract: PURPOSE:To simplify a device constitution by constituting a parallel/serial conversion circuit used for parallel/serial conversion in such a way that a part of picture element data among parallel picture element data obtained from Hadamard inverse transform is substituted for other picture element data. CONSTITUTION:An Hadamard inverse transform circuit 22 and the parallel/serial conversion circuit 23 are provided. For the circuit 22, a circuit outputting only x'13 being one component among picture element data x'00-x'13 which are originally obtained eight is used, and adders and subtractors requiring 24 devices in total so far can be simplified to only seven subtractors 22b. Picture data x'13 is supplied to the circuit 23 as represent of other picture element data x'00-x' , whereby only the output of data x'13 instead of them may be enough in a period when original data x'00-x'13 are outputted, and the constitution is simplified compared to a conventional parallel-serial conversion circuit.
Patent•
05 Sep 1988
TL;DR: In this article, the authors proposed a method to rapidly and properly determine the check time of subculture or antibody production, by dividing image data into blocks and selecting Hadamard transformation coefficient calculated from the data of each block to discriminate the presence of cell proliferation.
Abstract: PURPOSE:To rapidly and properly determine the check time of subculture or antibody production, by dividing image data into blocks and selecting Hadamard transformation coefficient calculated from the data of each block to discriminate the presence of cell proliferation. CONSTITUTION:The image from the image pickup apparatus 2 connected to a microscope 1 is digitalized to be stored in a frame memory 4. A block divider 5 divides the obtained image data into the designated number of blocks. An Hadamard converter 7 applies Hadamard transformation to the image data of each block to calculate Hadamard transformation coefficient which is, in turn, stored in an Hadamard transformation coefficient memory 8. A coefficient data selection means 9 selects coefficient data to be used from the memory 8 on the basis of the input from a selection data input means 10. A discrimination analytical means 11 compares said coefficient data with the reference value preset to a reference value memory and setting means to discriminate the presence of the cell proliferation of each block to store the same in a discriminated analytical result memory 14. A proliferation rate calculation means 15 calculates a proliferation rate from the stored presence of the cell proliferation of each block to output the same to an output apparatus 16.
TL;DR: In this paper, it was shown that the existence of circulant Hadamard matrices is not a given property of a (v, k, λ)-difference set when v is even.
Abstract: Summary In this paper we determine some properties concerning a (v, k, λ)-difference set when v is even. In particular it is proved in certain cases the non-existence of circulant Hadamard matrices.
Patent•
23 Dec 1988
TL;DR: In this paper, the authors proposed to reduce the capacity of a storage device by processing the measurement data of a multichannel detector by Hadamard transformation and then storing it in the storage device.
Abstract: PURPOSE:To reduce the capacity necessary for a storage device by processing the measurement data of a multichannel detector by Hadamard transformation and then storing it in the storage device. CONSTITUTION:A photodiode array 22 is driven by a driving circuit 24 and signals of respective photodetecting elements are led out in order and sent out to a preamplifier 26. The detection signals amplified by the preamplifier 26 are inputted to a CPU 30 through an A/D converter 28. The CPU 30 corrects the input measurement data by dark current correction, background correction, etc., performs the Hadamard transformation, and stores the resulting data in the memory 32. Further, the CPU reads the data out of the memory 32, performs reverse Hadamard transformation, and displays the data on a CRT 34.
TL;DR: A simple method for determining the sequency ordering of any row in any Hadamard matrix directly from its binary representation is developed, proved to be much simpler than the well-known bit-reverse inverse Gray code method.
Abstract: A simple method for determining the sequency ordering of any row in any Hadamard matrix directly from its binary representation is developed. This proposed method is proved to be much simpler than the well-known bit-reverse inverse Gray code method. >
01 Nov 1988
TL;DR: The paper introduces two methods for systematically reducing the signal correlation, and hence improving the so called ‘stability rate’ of a 2-D LPC system, based on the2-D Fourier transform and the Hadamard transform.
Abstract: Following the considerable success that linear predictive coding (LPC) has had in speech compression, the technique has been applied to the coding of two-dimensional (2-D) signals such as natural images. Unlike its one-dimensional (1-D) counterpart, the 2-D technique is not guaranteed to be stable. It is found that too much correlation in the signal causes a significant proportion of the analysis frames to produce unstable prediction filters, rendering the decoded image unintelligible. The paper introduces two methods for systematically reducing the signal correlation, and hence improving the so called ‘stability rate’ of a 2-D LPC system. The first method is based on the 2-D Fourier transform, and the second is based on the 2-D Hadamard transform. The effectiveness of each method is illustrated followed by a cost analysis based on algorithm complexity and bit-rate overhead.