Showing papers on "Hadamard transform published in 1979"

Video player and/or recorder with Hadamard transform

Abstract: An apparatus for performing a Hadamard transform on video data for compression of data to be recorded and decompression of data read from a record for display achieves the necessary high rate by means of two or more adders and two subtractors operating in parallel. A store that holds the data during successive passes through an arithmetic unit has accessing circuits and a set of registers and associated gates that fetch and store the data in a repetitive sequence that simplifies storage accessing. Data is processed in units that represent for example eight lines of a television picture and an output buffer is provided for the decompressor of a video disk player that receives data as it is processed and holds previously processed data unit by a storage accessing circuit that minimizes the amount of buffer storage that must be provided in the player.

Transform domain motion estimation

Abstract: This paper introduces an algorithm for estimating the displacement of moving objects in a television scene from spatial transform coefficients of successive frames. The algorithm works recursively in such a way that the displacement estimates are updated from coefficient to coefficient. A promising application of this algorithm is in motion-compensated interframe hybrid transform- dpcm image coding. We give a statistical analysis of the transform domain displacement estimation algorithm and prove its convergence under certain realistic conditions. An analytical derivation is presented that gives sufficient conditions for the rate of convergence of the algorithm to be independent of the transform type. This result is supported by a number of simulation examples using Hadamard, Haar, and Slant transforms. We also describe an extension of the algorithm that adaptively updates displacement estimation according to the local features of the moving objects. Simulation results demonstrate that the adaptive displacement estimation algorithm has good convergence properties in estimating displacement even for very noisy images.

On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms

Abstract: It is shown that the discrete Walsh–Hadamard transform applied to 2none-dimensional data is equivalent to the discrete n-dimensional Fourier transform applied to the same 2ndata arranged on the binary n-cube. A similar relationship is valid for the generalized discrete Walsh transform suggested by Andrews and Caspari. This relationship explains the theorem concerning the shift invariance of the power spectrum for the Walsh–Hadamard transform and its generalizations.

Higher-dimensional Hadamard matrices

Abstract: The concept of a Hadamard matrix as a binary orthogonal matrix is extended to higher dimensions. An n -dimensional Hadamard matrix [h_{ijk \cdots n}] is defined as one in which all parallel (n - 1) -dimensional layers, in any axis-normal orientation, are uncorrelated. This is equivalent to the requirements that h_{ijk \cdots n} = \pm1 and that \sum_{p} \sum_{q} \sum_{r} \cdots \sum_{y} h_{pqr \cdots yb}= m^{(n-1)} \delta_{ab} where (pqr \cdots yz) represents all permutations of (ijk \cdots n) . A "proper" n -dimensional Hadamard matrix is defined as a special case of the above in which all two-dimensional layers, in all axis-normal orientations, are Hadamard matrices, as a consequence of which all intermediate-dimensional layers are also Hadamard matrices. Procedures are described for deriving three- and four-dimensional Hadamard matrices of varying propriety from two-dimensional Hadamard matrices. A formula is given for a fully proper n -dimensional matrix of order two, which can be expanded by direct multiplication to yield proper (2^{t})^{n} Hadamard matrices. It is suggested that proper higher dimensional Hadamard matrices may find application in error-correcting cedes, where their hierarchy of orthogonalitias permit a variety of checking procedures. Other types of Hadamard matrices may be of use in security codes on the basis of their resemblance to random binary matrices.

Some remarks on generalised hadamard matrices and theorems of rajkundalia on sbibds

Abstract: Constructions are given for generalised Hadamard matrices and weighing matrices with entries from abelian groups.

Hadamard's variational formula for a mixed problem and an application to a problem related to a signorini-like variational inequality

Abstract: We give a variational formula for the solution of a Mixed Boundary Value Problem when the geometrical domain is perturbed (Hadamard's Variational Formula) ; we show that this formula contains singularities ; the result is used to construct a new approach to the optimal control problem for a problem related to a Signorini-like Elliptic Variational Inequality.

Coefficient extrapolator for the Haar, Walsh, and Hadamard domains

Abstract: In a data compression system utilizing the Haar, Walsh or Hadamard transformation, a machine which operates in the transform domain to obtain approximations to the higher order transform coefficients by means of extrapolation from lower order transform coefficients. The extrapolation of the higher order transform coefficients is approximately equivalent to either a linear or to a quadratic interpolation within the spatial or time domain.

Unified Matrix Treatment of Discrete Transforms

Abstract: An unified matrix treatment is developed for some discrete transforms such as Haar (HT), rationalized Haar (RHT), rapid (RT), modified Wash–Hadamard (MWHT), Hadamard– Haar (HHT)r, and rationalized Hadamard–Haar (RHHT)r. For RT a technique for recovering the data sequence from the transform vector is presented.

The Basic Theory of Hadamard Transform Spectrometers and Imagers

Abstract: If n small objects are weighed in clumps rather than one at a time, the accuracy of the weighings can be increased by a factor of n. This fact is the basis for Hadamard transform spectroscopy. In this chapter we show that the signal-to-noise ratio in measuring an n-element spectrum can in some cases be increased by a factor proportional to n . We also prove a number of new results about the optimal design of double encoding schemes for spectrometers and imagers, and compare these instruments with Michelson interferometers.

Higher-dimensional extensions of Pauli spin matrices

Abstract: The principle of basis set representation in terms of coordinate interchange matrices, of which the Pauli spin matrices are an example in two dimensions, are extended to three and four dimensions. The four-dimensional basis set of coordinate interchange matrices satisfies the usual conditions of completeness, but the three-dimensional basis set cannot be complete under any circumstances and an 'anticomplete' property is assigned to it. The coefficients of the basis set, when used to represent an arbitrary matrix, form a Hadamard transform of the cyclically interchanged arbitrary matrix.

Matrix multipliers for calculating orthogonal transforms

Abstract: The use of MOS transistors and weighted capacitors in a device to calculate the transform of a set of signal samples in 300ns will be discussed. Experimental results for a 16-point Hadamard and an 8-point complex Fourier transform will be given.

A data processor and method of processing video information

Abstract: A video player/recorder receives video information on line 12 to be recorded on a disk 28 or reproduced from the disk 28 for display on a television set 46. Prior to recording, the information is compressed in compactor 20 and following reproduction, the information is decompressed in decompactor 35. The information is prepared for compression by means of an arithmetic unit 17 and is processed following decompression by the same unit 17. The unit 17 performs a Hadamard transform on the video data and achieves the necessary high processing rate by means of two adders and two subtractors operating in parallel. A store 16 that holds the data during successive passes through the arithmetic unit 17 has accessing circuits and a set of registers and associated gates that fetch and store the data in a repetitive sequence that simplifies storage accessing. Data is processed in units that represent for example eight lines of a television picture and are supplied to an output buffer 41.

Conditional replenishment using motion prediction

Abstract: Conditional replenishment is an interframe video compression method that uses correlation in time to reduce video transmission rates. This method works by detecting and sending only the changing portions of the image and by having the receiver use the video data from the previous frame for the non-changing portion. The amount of compression that can be achieved through this technique depends to a large extent on the rate of change within the image, and can vary from 10 to 1 to less than 2 to 1. An additional 3 to 1 reduction in rate is obtained by the intraframe coding of data blocks using a 2-dimensional variable rate Hadamard transform coder. A further additional 2 to 1 rate reduction is achieved by using motion prediction. Motion prediction works by measuring the relative displacements of a subpicture from one frame to the next. The subpicture can then be transmitted by sending only the value of the 2-dimensional displacement. Computer simulations have demonstrated that data rates of 2 to 4 Mega-bits/second can be achieved while still retaining good fidelity in the image.

Waish-Hadamard Power Spectra Invariant to Certain Transform Groups

Abstract: Changes in Walsh-Hadamard power spectrum of an input pattern are investigated under several transformations: 1) shifting the elements of the input pattern cyclically, 2) enlarging and reducing the input pattern, 3) rotating the input pattern by multiples of 90°, and so on. Then the Walsh-Hadamard power spectrum is developed to be unchangeable by all the transformations through an introduced composing process. It may be considered as one of geometrical features. Every interesting geometrical property is generally invariant under some transformation groups. The composing process is available for obtaining functions having such group-invariant properties. The main idea is to make a linear combination of group-equivalent functions. First a G1-invariant power spectrum and next a permutation group on the G1-invariant power spectrum caused by G2 operating on the input pattern is found, thus arriving at a power spectrum being constant under both G1 and G2 through the composing process, where G1 and G2 are some transformation groups. Continuing this process, a power spectrum can be derived from the Walsh-Hadamard power spectrum that is invariant under a more general group of transformations.

An Efficient Algorithm for Determining Hadamard Sequency Vectors

Abstract: An efficient algorithm for determining the sequency vector S n of a 2n× 2nHadamard matrix is developed. The method requires fewer computation steps than a previously known method.

A Generalized Orthogonal Transformation Matrix

Abstract: A procedure is described for generating a two-parameter orthogonal transformation matrix which reduces to the Fourier and Hadamard transformation matrices under special conditions. This generalized transformation matrix is particularly useful for multidimensional signal processing on a real-time basis because it preserves a proper relationship in the transform domain.