Showing papers on "Hadamard transform published in 2001"

Transform-based image enhancement algorithms with performance measure

Abstract: This paper presents a new class of the "frequency domain"-based signal/image enhancement algorithms including magnitude reduction, log-magnitude reduction, iterative magnitude and a log-reduction zonal magnitude technique. These algorithms are described and applied for detection and visualization of objects within an image. The new technique is based on the so-called sequency ordered orthogonal transforms, which include the well-known Fourier, Hartley, cosine, and Hadamard transforms, as well as new enhancement parametric operators. A wide range of image characteristics can be obtained from a single transform, by varying the parameters of the operators. We also introduce a quantifying method to measure signal/image enhancement called EME. This helps choose the best parameters and transform for each enhancement. A number of experimental results are presented to illustrate the performance of the proposed algorithms.

A fast scheme for image size change in the compressed domain

Abstract: Given a video frame in terms of its 8/spl times/8 block-DCT coefficients, we wish to obtain a downsized or upsized version of this frame also in terms of 8/spl times/8 block-DCT coefficients. The DCT being a linear unitary transform is distributive over matrix multiplication. This fact has been used for downsampling video frames in the DCT domain. However, this involves matrix multiplication with the DCT of the downsampling matrix. This multiplication can be costly enough to trade off any gains obtained by operating directly in the compressed domain. We propose an algorithm for downsampling and also upsampling in the compressed domain which is computationally much faster, produces visually sharper images, and gives significant improvements in PSNR (typically 4-dB better compared to bilinear interpolation). Specifically the downsampling method requires 1.25 multiplications and 1.25 additions per pixel of original image compared to 4.00 multiplications and 4.75 additions required by the method of Chang et al. (1995). Moreover, the downsampling and upsampling schemes combined together preserve all the low-frequency DCT coefficients of the original image. This implies tremendous savings for coding the difference between the original frame (unsampled image) and its prediction (the upsampled image). This is desirable for many applications based on scalable encoding of video. The method presented can also be used with transforms other than DCT, such as Hadamard or Fourier.

A linear lower bound on the unbounded error probabilistic communication complexity

Abstract: We prove a general lower bound on the complexity of unbounded error probabilistic communication protocols. This result improves on a lower bound for bounded error protocols from Krause (1996). As a simple consequence we get the, to our knowledge, first linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions defined by Hadamard matrices. We also give an upper bound on the margin of any embedding of a concept class in half spaces.

Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime

Abstract: Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront set of their two-point functions (termed "wavefront set spectrum condition"), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance saling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

A generalized reverse jacket transform

Abstract: Generalization of the well-known Walsh-Hadamard transform (WHT), namely center-weighted Hadamard transform (CWHT) and complex reverse-jacket transform (CRJT) have been proposed and their fast implementation and simple index generation algorithms have recently been reported. These transforms are of size 2/sup r//spl times/2/sup r/ for integral values or r, and defined in terms of binary radix representation of integers. In this paper, using appropriate mixed-radix representation of integers, we present a generalized transform called general reverse jacket transform (GRJT) that unifies all the three classes of transforms, WHT, CWHT, and CRJT, and is also applicable for any even length vectors, that is of size 2/sup r//spl times/2/sup r/. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing error control codes.

The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson–Walker Spacetimes

Abstract: We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson–Walker spacetimes. Using this characterisation, we construct adiabatic vacuum states of order n corresponding to some Cauchy surface. It is demonstrated that any two such states (of sufficiently high order) are locally quasi-equivalent. We give a microlocal characterisation of spinor Hadamard states and we show that this agrees with the usual characterisation of such states in terms of the singular behaviour of their associated twopoint functions. The polarisation set of these twopoint functions is determined and found to have a natural geometric form. We finally prove that our adiabatic states of infinite order are Hadamard, and that those of order n correspond, in some sense, to a truncated Hadamard series and therefore allow for a point splitting renormalisation of the expected stress-energy tensor.

Capacity estimates for data hiding in compressed images

Abstract: We present an information-theoretic approach to obtain an estimate of the number of bits that can be hidden in still images, or, the capacity of the data-hiding channel. We show how the addition of the message signal or signature in a suitable transform domain rather than the spatial domain can significantly increase the channel capacity. Most of the state-of-the-art schemes developed thus far for data-hiding have embedded bits in some transform domain, as it has always been implicitly understood that a decomposition would help. Though most methods reported in the literature use DCT or wavelet decomposition for data embedding, the choice of the transform is not obvious. We compare the achievable data hiding capacities for different decompositions like DCT, DFT, Hadamard, and subband transforms and show that the magnitude DFT decomposition performs best among the ones compared.

2-D and 1-D multipaired transforms: frequency-time type wavelets

Abstract: A concept of multipaired unitary transforms is introduced. These kinds of transforms reveal the mathematical structure of Fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images. Considering paired transforms, we analyze simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one-dimensional (1-D) "signals", that determine such splitting. The main properties of the orthogonal system of paired functions are described, and the matrix decompositions of the Fourier and Hadamard transforms via the paired transforms are given. The multiplicative complexity of the two-dimensional (2-D) 2/sup r//spl times/2/sup r/-point discrete Fourier transform by the paired transforms is 4/sup r//2(r-7/3)+8/3-12 (r>3), which shows the maximum splitting of the 5-D Fourier transform into the number of the short 1-D Fourier transforms. The 2-D paired transforms are not separable and represent themselves as frequency-time type wavelets for which two parameters are united: frequency and time. The decomposition of the signal is performed in a way that is different from the traditional Haar system of functions.

System and method for computing and unordered Hadamard transform

Abstract: A system and method for parallel computation of the unordered Hadamard transform. The computing system includes a plurality of interconnected processors and corresponding local memories. An input signal x is received, partitioned into M1 sub-vectors xi of length M2, and distributed to the local memories. Each processor computer a Hadamard transform (order M2) on the sub-vectors in its local memory (in parallel), generating M1 result sub-vectors ti of length M2, which compose a vector t of length M1×M2. A stride permutation (stride M2) is performed on t generating vector u. Each processor computes a Hadamard transform (order M1) on the sub-vectors uj in its local memory (in parallel), generating M1 result sub-vectors vj of length M2, which compose a vector v of length M2×M1. A stride permutation is performed on v (stride M1) generating result vector w, which is the Hadamard transform of the input signal x.

Method and apparatus for non-linear code-division multiple access technology

Abstract: A class of n x l nonlinear block codes, termed Go-CDMA codes are constructed using column-reduced and row-reduced Hadamard orthogonal matrices, termed Go-CDMA matrices. Here n, l are positive integers: n chips of user data are transmitted in frames of size l ≤ α n, where α is the frame expansion factor. The codes map n-vectors containing binary messagedata to binary or multi-level l-vectors for transmission, where l ≥ n. The codes are invertible maps for the binary message data, and when there is no message data in some input vector elements, and noise added between the coding and decoding, there is some error correction. The coding uses integer arithmetic and integer quantization operations, preferably certain sign operations. Go-CDMA codes may be implemented in CDMA communication systems to improve performance on many measures over conventional CDMA and TDMA systems. The coding and decoding may include scrambling and descrambling the Go-CDMA coded signal based on random codes.

Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices

Abstract: We introduce Legendre sequences and generalised Legendre pairs (G L­ pairs). We show how to construct an Hadamard matrix of order 2£ + 2 from a GL-pair of length f. We review the known constructions for GL­ pairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable an exhaustive search for GL-pairs for lengths f ::::; 47 and partial searches for other f,

Novel FPGA implementations of Walsh-Hadamard transforms for signal processing

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.

The Existence of a Bush-Type Hadamard Matrix of Order 324 and Two New Infinite Classes of Symmetric Designs

Abstract: A symmetric 2-(324, 153, 72) design is constructed that admits a tactical decomposition into 18 point and block classes of size 18 such that every point is in either 0 or 9 blocks from a given block class, and every block contains either 0 or 9 points from a given point class. This design is self-dual and yields a symmetric Hadamard matrix of order 324 of Bush type, being the first known example of a symmetric Bush-type Hadamard matrix of order 4n^2 for n > 1 odd. Equivalently, the design yields a strongly regular graph with parameters v=324, k=153, \lambda=\mu=72 that admits a spread of cocliques of size 18. The Bush-type Hadamard matrix of order 324 leads to two new infinite classes of symmetric designs with parameters v=324(289^m+289^{m-1}+\cdots+289+1), \quad k=153(289)^m, \quad \lambda=72(289)^m, and v=324(361^m+361^{m-1}+\cdots+361+1), \quad k=171(361)^m, \quad \lambda=90(361)^m, where m is an arbitrary positive integer.

Genotype pattern recognition and classification

Abstract: Interpreting data obtained by analysis of nucleic acids (DNA) by obtaining nucleic acid data in a spatial domain, transforming the nucleic acid data from the spatial domain into a frequency domain, and obtaining sequence data of the nucleic acid data by executing a data mining process on the transformed nucleic acid data. The transformation may be performed by a Hadamard transform, a Fourier transform or a Wavelet transform to obtain frequency coefficients, with less than all of the frequency coefficients being utilized in the data mining process. In addition, the frequency domain data may be normalized prior to the data mining process. The data mining process may be subjecting the frequency coefficients to a connectionist (neural network) algorithm or to a classification tree/rule induction (CART) algorithm.

Bush‐type Hadamard matrices and symmetric designs

Abstract: Abstact: A symmetric 2-(100, 45, 20) design is constructed that admits a tactical decomposition into 10 point and block classes of size 10 such that every point is in either 0 or 5 blocks from a given block class, and every block contains either 0 or 5 points from a given point class. This design yields a Bush-type Hadamard matrix of order 100 that leads to two new infinite classes of symmetric designs with parameters and where m is an arbitrary positive integer. Similarly, a Bush-type Hadamard matrix of order 36 is constructed and used for the construction of an infinite family of designs with parameters and a second infinite family of designs with parameters where m is any positive integer. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 72–78, 2001

Optimization and characterization of an imaging Hadamard Spectrometer

Abstract: Hadamard Transform Spectrometer (HTS) approaches share the multiplexing advantages found in Fourier transform spectrometers. Interest in Hadamard systems has been limited due to data storage/computational limitations and the inability to perform accurate high order masking in a reasonable amount of time. Advances in digital micro-mirror array (DMA) technology have opened the door to implementing an HTS for a variety of applications including fluorescent microscope imaging and Raman imaging. A Hadamard transform spectral imager (HTSI) for remote sensing offers a variety of unique capabilities in one package such as variable spectral and temporal resolution, no moving parts (other than the micro-mirrors) and vibrational insensitivity. An HTSI for remote sensing using a Texas Instrument digital micro-mirror device (DMD) is being designed for use in the spectral region 1.25 - 2.5 micrometers . In an effort to optimize and characterize the system, an HTSI sensor system simulation has been concurrently developed. The design specifications and hardware components for the HTSI are presented together with results calculated by the HTSI simulation that include the effects of digital (vs. analog) scene data input, detector noise, DMD rejection ratios, multiple diffraction orders and multiple Hadamard mask orders.

Finite-Amplitude Waves in Mooney-Rivlin and Hadamard Materials

Abstract: These lectures deal with the the propagation of finite amplitude plane waves in Mooney-Rivlin and Hadamard elastic materials which are maintained in a state of arbitrary static homogeneous deformation. Exact plane wave solutions are presented for arbitrary propagation direction. The energy properties of these waves are investigated.

Masking, photobleaching, and spreading effects in Hadamard transform imaging and spectroscopy systems

Abstract: In analyzing the behavior of a Hadamard transform imaging spectroscopic system in an optical sectioning microscope, a previously undescribed masking effect was observed. During the process of characterizing this artifact, it was noted that while many masking errors have been reported previously in the literature, no attempt has been made to classify them or to systematically treat their effects in a variety of imaging and spectroscopy arrangements. Previous reports have documented echo artifacts in one-dimensional Hadamard mask systems based on sequences of length 2n - 1, for which the echoes are well defined. Other valid cyclic S-sequences, such as those of prime length 4m + 3 ≠ 2n - 1, do not exhibit such behavior. Masking errors may be present with these sequences, but they do not appear as echoes. Recovered intensities are observed having both positive and negative magnitude distributed throughout the transform axis. These masking defects appear superficially to be

Dual-Beam Near-Infrared Hadamard Spectrophotometer:

Abstract: A dual-beam Hadamard multiplexed spectrophotometer is described. The instrument is intended to work in the near-infrared region of the electromagnetic spectrum (900–1800 nm) and is based on the use of a linear Hadamard mask containing 255 multiplexing elements. Simple symmetric Czerny-Turner optics were employed based on 10 cm diameter, 20 cm focus spherical mirrors and a plane grating containing 295 grooves mm−1. The dual-path system employs the multiplexed beam exiting from the mask, which can then be split by using either an integrating sphere, a bifurcated optical bundle, or a beamsplitter. Two cooled PbS or InAs detectors were employed to collect the 255 multiplexed intensities in about 8 s. Signal was obtained by linear displacement of the mask, which was controlled by software written in VisualBasic 4.0. Spectral data were demultiplexed with a program written in the same language. The instrument can successfully correct for the drift of the light source intensity. The wavelength precision is 0.4 nm, while the average standard deviation for absorbance measurements taken from 900 to 1800 nm is 1.5 × 10−3 absorbance units, a value that is about three times lower than that obtained for the single-beam multiplexed approach. The instrument has been applied to the determination of water in fuel ethanol with the use of partial least-squares modeling. The absolute standard error of prediction was 0.07% (w/w).

Decision diagram method for calculation of pruned Walsh transform

Abstract: Discrete Walsh transform is an orthogonal transform often used in spectral methods for different applications in signal processing and logic design. FFT-like algorithms make it possible to efficiently calculate the discrete Walsh spectrum. However, for their exponential complexity, these algorithms are practically unsuitable for large functions. For this reason, a Binary Decision Diagram (BDD) based recursive method for Walsh spectrum calculation has been introduced in Clarke et al. (1993). A disadvantage of this algorithm is that the resulting Multi-Terminal Binary Decision Diagram (MTBDD) representing the Walsh spectrum for f can be large for some functions. Another disadvantage turns out if particular Walsh coefficients are to be computed separately. The algorithm always calculates the entire spectrum and, therefore, it is rather inefficient for applications where a subset of Walsh spectral coefficients, i.e., the pruned Walsh spectrum, is required. In this paper, we propose another BDD-based method for Walsh spectrum calculation adapted for application where the pruned Walsh spectrum is needed. The method takes advantage of the property that for most switching functions, the size of a BDD for f is usually quite a bit smaller than the size of the MTBDD for the Walsh spectrum. In our method, a MTBDD representing the Walsh spectrum is not: constructed. Instead, two additional fields are assigned to each node in the BDD for the processed function f. These fields are used to store the results of intermediate calculations. Pairs of spectral coefficients are calculated and stored in the fields assigned to the root node. Therefore, the calculation complexity of the proposed algorithm is proportional to the size of the BDD for f whose spectrum is calculated. Experimental results demonstrate the efficiency of the approach.

How Tight is Hadamard's Bound?

Abstract: For a real square matrix $M$, Hadamard's inequality gives an upper bound $H$ for the determinant of $M$; the bound is sharp if and only if the rows of $M$ are orthogonal. We study how much we can expect that $H$ overshoots the determinant of $M$, when the rows of $M$ are chosen randomly on the surface of the sphere. This gives an indication of the "wasted effort'' in some modular algorithms.

Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming

Abstract: In this paper we introduce the concept of solving strategy for a linear semi-infinite programming problem, whose index set is arbitrary and whose coefficient functions have no special property at all. In particular, we consider two strategies which either approximately solve or exactly solve the approximating problems, respectively. Our principal aim is to establish a global framework to cope with different concepts of well-posedness spread out in the literature. Any concept of well-posedness should entail different properties of these strategies, even in the case that we are not assuming the boundedness of the optimal set. In the paper we consider three desirable properties, leading to an exhaustive study of them in relation to both strategies. The more significant results are summarized in a table, which allows us to show the double goal of the paper. On the one hand, we characterize the main features of each strategy, in terms of certain stability properties (lower and upper semicontinuity) of the feasible set mapping, optimal value function and optimal set mapping. On the other hand, and associated with some cells of the table, we recognize different notions of Hadamard well-posedness. We also provide an application to the analysis of the Hadamard well-posedness for a linear semi-infinite formulation of the Lagrangian dual of a nonlinear programming problem.

Highly Multiplexed Optically Sectioned Spectroscopic Imaging in a Programmable Array Microscope

Abstract: We report the construction of a spectroscopic programmable array microscope capable of optical sectioning using Hadamard transform methods. Previously described Hadamard transform imaging consisted of first-order systems in which the mask was used for either illumination or detection. In this paper, a second-order Hadamard transform system is described in which a single one-dimensional mask serves for both illumination and detection. The system verifies earlier predictions that the optical spreading function along the transform axis can be inferred from the echoes arising in second-order systems using sequence lengths of 2n-1. With a one-dimensional Hadamard mask, the system has an axial resolution of 1.3 μm and may be used with or without the subtraction of an appropriately scaled wide field image depending on the degree of sectioning required. The system was tested using thin films, fluorescent beads, and a fixed biological specimen.