Showing papers on "S transform published in 1999"

Efficient time series matching by wavelets

Abstract: Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases.

Transform domain analysis of DES

Abstract: The Data Encryption Standard (DES) can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under the Fourier transform, Hadamard transform, extended Hadamard transform, and the Avalanche transform are investigated. Two important results about the S-boxes of DES are found. The first result is that nearly two-thirds of the total 32 functions from GF (2/sup 6/) to GF(2) which are associated with the eight S-boxes of DES have the maximal linear span G3, and the other one-third have linear span greater than or equal to 57. The second result is that for all S-boxes, the distances of the S-boxes approximated by monomial functions has the same distribution as for the S-boxes approximated by linear functions. Some new criteria for the design of permutation functions for use in block cipher algorithms are discussed.

On the inverse Hough transform

Abstract: In this paper, an inverse Hough transform algorithm is proposed. This algorithm reconstructs correctly the original image, using only the data of the Hough transform space and it is applicable to any binary image. As a first application, the inverse Hough transform algorithm is used for straight-line detection and filtering. The lines are detected not just as continuous straight lines, which is the case of the standard Hough transform, but as they really appear in the original image, i.e., pixel by pixel. To avoid the quantization effects in the Hough transform space, inversion conditions are defined, which are associated only with the dimensions of the images. Experimental results indicate that the inverse Hough transform algorithm is robust and accurate.

SAR image compression with the Gabor transform

Abstract: A compression system based on the Gabor transform is applied to detected synthetic aperture radar (SAR) imagery. The Gabor transform is a combined spatial-spectral transform that provides local spatial-frequency analyses in overlapping neighborhoods of the image. Gabor coefficients are efficiently computed using the fast Fourier transform (FFT), and a technique for visualizing the coefficients is demonstrated. Theoretical and practical constraints imposed by the Gabor transform are discussed. The compression system includes bit allocation, quantization, and lossless encoding and decoding stages. Bit allocation tradeoffs are discussed and related to perceptual image quality as well as computational measures of image fidelity. Adaptive scalar, vector, and trellis-coded quantizers are compared. Multifrequency codebooks are designed using ten training images derived from data collected at different aspect angles. Subjective image quality assessment experiments indicate that the Gabor transform/trellis-coded quantizer compression system performs significantly better than adaptive scalar and vector quantizers and JPEG on these SAR images.

Rotation of NMR images using the 2D chirp-z transform.

Abstract: A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpolation to get the final real-space image in the conventional way. The rotation angle and shift distances are embedded in the parameters of the chirp-z transform. The chirp-z transform implements discrete sinc interpolation to get values at grid points that are not exactly on the original grid when applying the inverse Fourier transform. Therefore, the chirp-z transform is more accurate than methods such as linear or bicubic interpolation and is more efficient than direct implementation of sinc interpolation because the sinc interpolation is implemented at the same time as reconstruction from k-space.

Optimized quadtree for Karhunen-Loeve transform in multispectral image coding

Abstract: A new multispectral image compression technique based on the Karhunen-Loeve transform (KLT) and the discrete cosine transform (DCT) is proposed. The quadtree for determining the transform block size and the quantizer for encoding the transform coefficients are jointly optimized in a rate-distortion sense. The problem is solved by a Lagrange multiplier approach. After a quadtree is determined by this approach, a one-dimensional (1-D) KLT is applied to the spectral axis for each block before the DCT is applied on the spatial domain. The eigenvectors of the autocovariance matrix, the quantization scale, and the quantized transform coefficients for each block are the output of the encoder. The overhead information required in this scheme is the bits for the quadtree, KLT, and quantizer representation.

A unified reconstruction framework for both parallel-beam and variable focal-length fan-beam collimators by a Cormack-type inversion of exponential Radon transform

Abstract: A variety of inversions of exponential Radon transform has been derived based on the circular harmonic transform in Fourier space by several research groups. However, these inversions cannot be directly applied to deal with the reconstruction for fan-beam or variable-focal-length fan-beam collimator geometries in single photon emission computed tomography (SPECT). In this paper, the authors derived a Cormack-type inversion of the exponential Radon transform by employing the circular harmonic transform directly in the projection space and the image space instead of the Fourier space. Thus, a unified reconstruction framework is established for parallel-, fan-, and variable-focal-length fan-beam collimator geometries. Compared to many existing algorithms, the presented one greatly mitigates the difficulty of image reconstruction due to the complicated collimator geometry and significantly reduces the computational burden of the special functions, such as Chebyshev or Bessel functions. By the well-established fast-Fourier transform (FFT), the authors' algorithm is very efficient, as demonstrated by several numerical simulations.

Direct transform to transform computation

Abstract: An efficient direct method for the computation of a length-N discrete cosine transform (DCT) given two adjacent length-(N/2) DCT coefficients, is presented. The computational complexity of the proposed method is lower than the traditional approach for lengths N>8. Savings of N memory locations and 2N data transfers are also achieved.

Transform domain algorithm for reducing effect of film-grain noise in image compression

Abstract: An algorithm for decreasing the effect of film-grain noise in image compression is proposed. The algorithm operates in the transform domain in conjunction with quantisation. Although any orthogonal transform is suitable for this application, the orthogonal wavelet transform is preferred due to the simplicity in calculating the filter coefficients.

A survey of mixed transform techniques for speech and image coding

Abstract: The goal of transform based coding is to build a representation of a signal using the smallest number of weighted basis functions possible, while maintaining the ability to reconstruct the signal with adequate fidelity. Mixed transform techniques, which employ subsets of non-orthogonal basis functions chosen from two or more transform domains, have been shown to consistently yield more efficient signal representations than those based on one transform. This paper provides a survey of mixed transform techniques, also known as multitransforms or mixed basis representations, which have been developed for speech and image coding.

A new class of fast shape-adaptive orthogonal transforms and their application to region-based image compression

Abstract: Region-based approaches to image and video compression have been very actively explored in the last few years. It is widely expected that they will result in rate/quality gains and expanded functionalities. In such approaches, one of the essential problems is the representation of luminance and color in arbitrarily shaped regions. For rectangular blocks extracted from natural images, the discrete cosine transform (DCT) has been found to perform close to the eigentransform. Although for arbitrarily shaped regions orthogonalization-based procedures have been shown to perform very well, their computational complexity and memory requirements are prohibitive for today's technology. Therefore, other approaches are presently investigated, and particular attention is paid to low implementation complexity. In this paper, we propose a new class of orthogonal transforms that self-adapt to arbitrary shapes. The new algorithms are derived from flow graphs of standard fast transform algorithms by a suitable modification of certain butterfly operators. First, we show how to derive a shape-adaptive transform from the discrete Walsh-Hadamard transform (DWHT) flow graph. Then, we discuss modifications needed to arrive at a DCT-based shape adaptive transform. We give implementation details of this transform, and compare its computational complexity with several well-known approaches. We also evaluate the energy compaction performance of the new transform for both synthetic and natural data. We conclude that the proposed DCT-based shape-adaptive transform gives a very beneficial compaction/complexity ratio compared to other well-known approaches. The complexity of the new method does not exceed the complexity of two nonadaptive DCT's on a circumscribing rectangle, and therefore, unlike other tested methods with comparable energy compaction, it is suitable for large regions. This property should prove very valuable in the future when true region-based image/video compression methods are developed.

New properties of the Radon transform of the cross Wigner/ambiguity distribution function

Abstract: In this correspondence, we prove that the Radon transform of the cross Wigner distribution function is a separable multiplication of fractional Fourier transforms of these functions. Thus, the 2-D cross ambiguity function is a surface of fractional correlation for 1-D signals, each associated with the angle of observation over the surface.

Passive wideband cross correlation with differential Doppler compensation using the continuous wavelet transform

Abstract: An estimate of the time difference for the signal emitted by a stationary source to arrive at two spatially separated sensors is given by the time displacement that maximizes the cross-correlation function. For a fast moving source, however, this estimate is found to be in error because the time scales of the received signals are different for the two sensors. The correct time delay can be extracted by evaluating the continuous wavelet transform, which has the same functional form as the wideband cross-ambiguity function. When the signal-to-noise ratio is high, the coordinates of the ambiguity surface’s global maximum provide reliable estimates of both the differential time of arrival (or time delay) and the ratio of the time scales of the signals received by the two sensors. The continuous wavelet transform is computed using the one-step chirp z-transform method, the cross-wavelet transform method, and the two-step methods where multirate sampled replicas of the sensor waveforms are cross correlated, or ...

On the Spectral Density of the Wavelet Transform of Fractional Brownian Motion

Abstract: We consider the wavelet transform {Wa(t), −∞ 0, of a fractional Brownian motion. A simple and mathematically rigorous proof is given to establish the existence of the spectral density fWa(λ) of the wavelet transform and provide an expression for it.

The 2-D wavelet transform, physical applications and generalizations

Abstract: We begin with a short review of the 2-D continuous wavelet transform (CWT) and describe a number of physical applications. Then we discuss briefly the mathematical background, namely coherent states derived from group representations, and we show how it allows a straightforward extension to more general situations, such as higher dimensions, wavelets on the sphere or time-dependent wavelets. We conclude with a short outline of the 2-D discrete wavelet transform, some generalizations and a few physical applications.

Defect Detection in Fabrics with a Joint Transform Correlation Technique: Theoretical Basis and Simulation:

Abstract: The theoretical basis of a technique for real time defect detection in fabrics is presented using a joint transform correlator. This correlation technique is an extension of Fourier transform analysis and is extremely useful for real time pattern recognition. The regular periodic nature of a woven fabric makes it possible to use the Fourier transform technique to detect defects. However, classifying various defect types is difficult from the Fourier analytical and experimental results. A solution to this problem is to use a joint Fourier transform of a reference pattern and the test pattern, and the joint power spectrum is further processed. Cross- and auto-correlation peaks, generated after the execution of the second Fourier transform on the filtered joint power spectrum, indicate the existence of a particular defect type. Because of the parallel processing ability of the optical system, implementing the joint transform correlation technique in an optical domain is advanta geous. A fractional power frin...

Lapped directional transform: a new transform for spectral image analysis

Abstract: We propose a new real-valued lapped transform for 2D-signal and image processing Lapped transforms are particularly useful in block-based processing, since their intrinsically overlapping basis functions reduce or prevent block artifacts Our transform is derived from the modulated lapped transform (MLT), which, as a real-valued and separable transform like the discrete cosine transform, does not allow to unambiguously identify oriented structures from modulus spectra This is in marked contrast to the (complex-valued) discrete Fourier transform (DFT) The new lapped transform is real-valued, and at the same time allows unambiguous detection of spatial orientation Furthermore, a fast algorithm for this transform exists As an application example, we investigate the transform's performance in spectral approaches to image restoration and enhancement in comparison to the DFT

Optimized Fast Algorithms for the Quaternionic Fourier Transform

Abstract: In this article, we deal with fast algorithms for the quaternionic Fourier transform (QFT). Our aim is to give a guideline for choosing algorithms in practical cases. Hence, we are not only interested in the theoretic complexity but in the real execution time of the implementation of an algorithm. This includes floating point multiplications, additions, index computations and the memory accesses. We mainly consider two cases: the QFT of a real signal and the QFT of a quaternionic signal. For both cases it follows that the row-column method yields very fast algorithms. Additionally, these algorithms are easy to implement since one can fall back on standard algorithms for the fast Fourier transform and the fast Hartley transform. The latter is the optimal choice for real signals since there is no redundancy in the transform. We take advantage of the fact that each complete transform can be converted into another complete transform. In the case of the complex Fourier transform, the Hartley transform, and the QFT, the conversions are of low complexity. Hence, the QFT of a real signal is optimally calculated using the Hartley transform.

Multidimensional polynomial transform algorithm for multidimensional discrete W transform

Abstract: The multidimensional (MD) polynomial transform is used to convert the MD W transform (MDDWT) into a series of one-dimensional (1-D) W transforms (DWTs). Thus, a new polynomial transform algorithm for the MDDWT is obtained. The algorithm needs no operations on complex data. The number of multiplications for computing an r-dimensional DWT is only 1 times that of the commonly used row-column method. The number of additions is also reduced considerably.

Wavelet transform method and apparatus

Abstract: An image signal encoded for compression using a wavelet transform as a transform system is to be decoded at a resolution corresponding to an optional rational number. To this end, the wavelet decoding device includes an entropy decoding unit 1 for entropy decoding an encoded bitstream 100 , a dequantizing unit for dequantizing the quantized coefficients 101 to transmit transform coefficients 102 , a transform coefficient back-scanning unit 3 for scanning the transform coefficients 102 in a pre-set fashion to re-array the transform coefficients, and an inverse wavelet transform unit 4 for inverse transforming the re-arrayed transformation coefficients 103 to furnish a decoded image 104 . The inverse wavelet transform unit 4 adaptively constitutes an upsampler, a downsampler and a synthesis filter in dependence upon a pre-set resolution conversion factor.

Hartley transform in compression of medical ultrasonic images

Abstract: In this paper the Hartley transform has been used for both compression and filtering of medical ultrasonic images. The Hartley transform shares some features of the Fourier transform and, most importantly, there exists a computationally effective butterfly algorithm of the transform. Compression relies on filtering out higher harmonics of the forward Hartley transform and saving the result rather as the image than the coefficients of the transform. In this case the images' size is reduced 16 times without significant loss of valuable medical information.

Multiple description coding via scaling-rotation transform

Abstract: We propose a two-stage transform design technique for multiple description transform coding. The first stage is the structure design in which we enforce a scaling-rotation factorization of the transform and we further constrain the transform for specific channel conditions using the knowledge of the input correlation matrix and the desired output correlation matrix. In the second stage, magnitude design, we find the optimal transform from all admissible transforms given by the structure design using the numerical algorithm proposed by Goyal et al. (see Proc. of IEEE Data Compression Conference, 1998). Such a design enables a structured transform framework which reduces both the design and implementation complexities compared to an exhaustive search through the whole space of nonorthogonal transforms. We give two examples to illustrate the design idea, the scaling-Hadamard transform for equal rate channels and the scaling-DST transform for sequential protection channels.

Generalized dual-point Hough transform for object recognition

Abstract: In this paper, a modified version of dual-point generalized Hough transform has been proposed. Inspired by the result of an analysis of the shapes of objects, we are able to improve the efficiency of the dual-point generalized Hough transform. A characteristic angle, which is governed by the points selected in the recognition process, will be determined for the generation of the R-table. This angle is based on making the number of index entries in the R-table as large as possible, the number of entries per indexes as small as possible, and the number of access per point as small as possible. Experimental results show that it can improve the transform by increasing the detection accuracy and speed after the modification is made into the transform.

A novel multiwavelet-based integer transform for lossless image coding

Abstract: Integer Haar wavelet transform or S-transform is used as the basic building block for many exiting integer wavelet transform. As an alternative, a new integer multiwavelet transform and its associated integer prefilter are designed based on box-and-slope multi-scaling system. Both the transform and prefilter can be implemented with simple integer Haar transform requiring only addition and bit shift operations. Since the new integer transform is an approximation to nontruncated transform with higher vanishing moment than that of Haar transform, better approximation accuracy is expected and verified experimentally. The transform is successfully applied to lossless image coding with results outperforming that of lossless JPEG and S-transform.

Comment on “Time-frequency analysis with the continuous wavelet transform,” by W. Christopher Lang and Kyle Forinash [Am. J. Phys. 66 (9), 794–797 (1998)]

Abstract: We read with much interest the paper by Lang and Forinash ~Ref. 1! but felt we needed to add words of caution regarding wavelet analysis. We state at the outset, though, it is not our intent to either blemish or deny the results of Lang and Forinash. We do, however, want to make clear that, when applied to well-defined problems, wavelets work wonders. When applied, on the other hand, to less well-defined problems, the wavelet transformdoes not always‘‘produce spectrograms which show the frequency content of sounds ~or other signals ! as a function of time in a manner analogous to sheet music.’’ The analysis in Ref. 1 is indeed accurate and to the point and produces the desired results in the cases described there because the signals analyzed were artificially created; consequently, their pitch and frequency content were known a priori . In phenomena where intensity and frequency content are not knowna priori, such as turbulent flows and other random signals, the wavelet transform often obscures significant information in the signal. As an example, a wavelet that is a second-difference operator, such as the French-hat wavelet, can provide no information on the linear trend in a signal. For the unfamiliar reader, the French-hat wavelet is defined as$2B(3a)12B(3a21)2B(3a22)%/2AL, where a5t/L and B(a) is the standard box function. That is, B(a)51 for 0

Optimal transform coding in the presence of quantization noise

Abstract: The optimal linear Karhunen-Loeve transform (KLT) attains the minimum reconstruction error for a fixed number of transform coefficients assuming that these coefficients do not contain noise. In any real coding system, however, the representation of the coefficients using a finite number of bits requires the presence of quantizers. We formulate the optimal linear transform using a data model that incorporates the quantization noise. Our solution does not correspond to an orthogonal transform and in fact, it achieves a smaller mean squared error (MSE) compared to the KLT, in the noisy case. Like the KLT, our solution depends on the statistics of the input signal, but it also depends on the bit-rate used for each coefficient. Especially for images, based on our optimality theory, we propose a simple modification of the discrete cosine transform (DCT). Our coding experiments show a peak signal-to noise ratio (SNR) performance improvement over JPEG of the order of 0.2 dB with an overhead less than 0.01 b/pixel.

Hilbert transform in image processing

Abstract: Generally, the Hilbert transform plays an important role in dealing with analytical functions. Its main contribution to the signal processing era is to change electrical signals to be of low-pass style instead of band-pass. Image signals are commonly considered as of electrical nature and thus committed to this concept. The Fourier spectrum of images can be contributed to the Hilbert transform to yield /spl plusmn/90/spl deg/-phase shift in both sides of the spectrum. One dimensional Hilbert transform can be utilized to handle image signals in TVs and videos transmissions, while on the other hand, two dimensional Hilbert transform should be adopted in digitized and off-line imaging applications. The prime concern of this paper is to bring focus on these concepts by using simulations.

Iterative block-median pyramid transform-based denoising

Abstract: A nonlinear block-median pyramidal transform has been proposed. This transform is based on the iterative application of the median operation and linear Lagrange interpolation. The probability distribution of the transform coefficients has been analytically derived for i.i.d. input signals. The results of this statistical analysis are used for selecting the thresholds for denoising applications. Numerical simulation results are presented.

Multiridge Detection and

Abstract: The ridges of the wavelet transform, the Gabor transform, or any time-frequency representation of a signal contain crucial information on the characteristics of the signal. Indeed, they mark the regions of the time-frequency plane where the signal concentrates most of its energy. We introduce a new algorithm to detect and identify these ridges. The procedure is based on an original form of Markov chain Monte Carlo algorithm especially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multiridge transforms. It is a common practice among practitioners to reconstruct a signal from the skeleton of a transform of the signal (i.e., the restriction of the transform to the ridges.) After reviewing several known procedures, we introduce a new reconstruction algorithm, and we illustrate its efficiency on speech signals and its robustness and stability on chirps perturbed by synthetic noises at different SNR's. was motivated by the desire to handle low SNR's. We also note that bilinear representations such as the (generalized) Wigner distributions (3), (9) can be extremely precise in the one-component case but may completely fail in the multicom- ponent situation because of interference terms. We describe here a new approach capable of handling multiple component signals. This new approach is based on a new Markov chain Monte Carlo (MCMC) approach, which uses the energetic distribution provided by a time-frequency representation of the signal. Given the fact that the energy of the signal concentrates around curves in the time-frequency plane, which we shall call "ridges," the Markov chain is constructed in such a way that the random walkers (hereafter called "crazy climbers") are at- tracted by these 1-D structures. The analysis is complemented by an "synthesis step" devoted to the reconstruction of the "part(s)" of the signal that produced the ridge(s). Throughout the paper, the discussion is restricted to the cases of the Gabor and wavelet transforms. Notice that since our detection algorithm is only a special postprocessing of a time-frequency transform, it can be used with other time-frequency energetic representations, for example, the family of Wigner distributions discussed in (1). On the contrary, the reconstruction algorithm is specific to the representations. We develop it for wavelet and Gabor transforms, but the modifications required to extend it to other linear time-frequency representations are straightforward. The thrust of the present paper is twofold. First, we give a new ridge detection algorithm that can efficiently detect multiple ridges in the modulus of a transform, and second, we propose a signal reconstruction procedure from the knowledge of the skeleton of the transform on arbitrary points of its ridges. Our detection procedure is based on an original Markov chain Monte Carlo algorithm. It is designed in such a way that weighted occupation densities draw the ridges on the time-frequency plane. Most importantly, its robustness to noise is remarkable. The reconstruction procedure is restricted to linear transforms. It is based on the classical idea of spline smoothing as presented in (20). We already used it in the case of the wavelet transform (without much explanation) in the companion correspondence (5). We present it in full detail here. As for the ridge detection, it performs very well in noisy situations. Both components of our work (ridge detection and reconstruction) are illustrated on two specific data sets. The first one is the superposition of a real life sonar bat signal with an artificially generated chirp. It is analyzed with the wavelet transform. The second one is the speech recording considered in (14). We analyze it using the Gabor transform.