Showing papers on "S transform published in 1995"

The chirplet transform: physical considerations

Abstract: We consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving rise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a "time-frequency-scale volume" and thus encompasses both the short-time Fourier transform (as a slice along the time and frequency axes) and the wavelet transform (as a slice along the time and scale axes). In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear in time (obtained through convolution with a q-chirp) and shear in frequency (obtained through multiplication by a q-chirp). Signals in this multidimensional space can be obtained by a new transform, which we call the "q-chirplet transform" or simply the "chirplet transform". The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, which are related to each other by 1-D affine coordinate transformations (translations and dilations) in the time domain only.

A factorization method for the 3D X-ray transform

Abstract: We consider the inversion of the three-dimensional (3D) X-ray transform with a limited data set containing the line integrals which have two intersections with the lateral surface of a cylindrical detector The usual solution to this problem is based on 3D filtered-backprojection, but this method is slow This paper presents a new algorithm which factors the 3D reconstruction problem into a set of independent 2D radon transforms for a stack of parallel slices Each slice is then reconstructed using standard 2D filtered-backprojection The algorithm is based on the application of the stationary-phase approximation to the 2D Fourier transform of the data, and is an extension to three dimensions of the frequency-distance relation derived by Edholm et al(1986) for the 2D radon transform Error estimates are also obtained

Fractional Fourier transform used for a lens-design problem.

Abstract: The fractional Fourier transform has been used in optics so far for wave propagation and for signal processing. Now we show that this new transform can also be helpful for lens design, especially for specifying a lens cascade.

Fractional Fourier transform: simulations and experimental results

Abstract: Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.

Identification and synthesis of acoustic scattering components via the wavelet transform

Abstract: An acoustic scatterer can be described in the time domain by its impulse response function, or in the frequency domain by its form function. Both functions will contain several complementary and distinct components, none of which is fully separable in either the time or frequency domain. This renders Fourier based methods ineffective in identifying and extracting one component from all the others. However, it is possible to do this using the wavelet transform, a transform that yields a two‐dimensional (two‐parameter) representation of a signal. In this paper, this transform is used to identify and extract the acoustic components from physical model data.

Parallelizing the fast wavelet transform

Abstract: Two new algorithms for the Fast Wavelet Transform on parallel computers are presented. They are compared to a previously published algorithm [3,4] and are found to outperform this algorithm for a Connection Machine (CM) Fortran implementation of a two-dimensional wavelet transform on a CM-200 and a CM-5.

Fast Hankel transform of order zero

Abstract: An analytical form is presented that provides a clear and computationally efficient algorithm for numerically evaluating the Hankel transform of order zero by fast-Fourier-transform techniques.

Discrete scale transform for signal analysis

Abstract: The scale transform introduced by Cohen (see IEEE Trans. Signal Processing, vo1.41, p.3275-3292, December 1993) is a special case of the Mellin transform. The scale transform has mathematical properties desirable for comparison of signals for which scale variation occurs. In addition to the scale invariance property of the Mellin transform many properties specific to the scale transform have been presented. A procedure is presented for complete implementation of the scale transformation for discrete signals. This complements discrete Mellin transforms and delineates steps whose implementation are specific to the scale transform.

The Mellin-wavelet transform

Abstract: Most machine speech analysis and processing is based on a warped spectral representation. The intent of the paper is to present a method by which proper warped representations can be computed efficiently. In the case of log-warping functions, the methods of the paper produce a wavelet-like transform as a linear convolution of a single log-warped wavelet basis element and a log-warped representation of the signal. The resulting doubly warped transform is referred to in the paper as a Mellin-wavelet transform. The majority of the paper is devoted to deriving design parameters for implementation of the transform, with speech as the primary application.

An efficient structure and algorithm for the mixed transform representation of signals

Abstract: Mixed transform coders have been shown to consistently yield higher signal quality than those based on one transform for a fixed compression ratio. However, these coders have not been widely employed due to the very high computational complexity of formulations. This paper presents a new parallel mixed transform technique employing a novel projection algorithm for signal representation. Formulations are derived, algorithms are described and results of simulations are presented. Excellent performance is achieved with much less computation than required by existing mixed transform techniques, making real-time implementations possible.

Application of the discrete Laguerre transform to speech coding

Abstract: The discrete Laguerre transform (DLT) displays characteristics which make it amenable to the coding of speech. In this paper, the DLT is used in a classic transform coding method for speech and compared to the discrete cosine transform (DCT), which has been widely applied to speech coding. The results show promise, as the DLT outperforms the DCT at very low bitrates.

New separable transform

Abstract: A separable version in two dimensions of the transform previously presented by Boussakta and Holt (1992) is introduced and generalised to the multi-dimensional case. This transform is fast and symmetric, has the convolution property and is separable, making if a good candidate for the calculation of two-dimensional convolutions and correlations for image processing purposes.

Gabor wavelet filters and fusion for distortion-invariant multiclass object detection

Abstract: Several different new Gabor wavelet filters are described: the Gabor transform (GT) filter consists of real, imaginary, and clutter filters; the Gabor basis function (GBF) filter uses a Gabor basis function for each training image; the morphological wavelet transform (MWT) filter includes a Gabor transform clutter map filter that locates clutter regions of a scene. These filters ar all shift-invariant and distortion-invariant. They are employed for detection: location of the positions of all object regions of interest (ROIs) in an input scene. Fusion of multiple filter outputs is used to reduce false alarms. This paper emphasizes the role for Gabor wavelet filters in detection and for producing a clutter map. Major emphasis is given to the final version of the Gabor wavelet clutter map portion of our MWT algorithm (this is our best detection algorithm). New detection and fusion results with a consistent database and thresholds are provided.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

On invertibility of the windowed Radon transform

Abstract: The idea of the Windowed Radon Transform (WRT) was first introduced by G.Kaiser. This transform is interpreted as a generalization of several transforms. In this article, taking WRT for a generalized wavelet transform, we show that its invertion formula holds in various senses.

Self-Fourier objects and other self-transform objects: comment

Abstract: The sech function is an important example of a self-Fourier transform function that may have applications in the analysis of linear and nonlinear optical propagation.

Signal representation using adaptive parallel mixed transform techniques

Abstract: Transform based signal representations are central to lossy compression methods. Since most signals of interest contain both narrow and broad band frequency components, mixed transform techniques can frequently provide more efficient representations of such signals than individual transforms. This paper presents a new adaptive parallel mixed transform technique for signal representation. Formulations are derived, algorithms are described and results of simulations applied to speech signals are presented. Excellent performance is achieved with much less computation than required by existing mixed transform techniques, making real-time implementations feasible.

Time-frequency analysis of the second heart sound signals

Abstract: The difference of the properties of the Short Fourier Transform, Continuous Wavelet Transform and AR Spectra Array in time-frequency analysing for heart sound signals are studied and compared here. Some problems for using these methods are discussed. It is concluded that the Continuous Wavelet Transform has the highest property in representing the time-frequency distribution of the heart sound signals among these three methods.

Wavelet localized Radon transform

Abstract: A new transform which combines the key features of the Radon transform with the localization abilities of the wavelet transform is presented. The transform was developed in response to the problem of wake detection in open water synthetic aperture radar (SAR) images. Consider the fact that wakes are generally small in size relative to the original SAR image. Further, ship wakes have linear features. So even though the orientation and size of the wake is unknown a priori, a transform which has parameters for rotation and spatial localization may aid in the detection of these features.

A new 3-D transform using a ternary product

Abstract: We introduce a 3-D discrete transform that depends on the choice of a certain pair of 3-D arrays called inverse pairs. Many choices of inverse pairs are possible, and each choice gives a new 3-D transform. A number of new 2-D and 1-D transforms are also derived.

Modified short-time Fourier transform

Abstract: The short-time Fourier transform (STFT) is a typical time-frequency 2-D analysis method for nonstationary signals. Its applications in engineering are limited because of its fixed window, which results in low time-frequency resolution. To surmount this disadvantage, a modified short-time Fourier transform (MSTFT) is proposed. The minimum entropy is adopted as a criterion to determine the width of the window, and variable-width windows to accommodate the signal's characteristics are used instead of constant-width windows. Since it is difficult to find the optimal window width, wavelet packet transformation is utilized to find an approximate solution for it. This method is also applied to multi-target imaging for inverse synthetic aperture radar, and satisfactory results are achieved.

Linear Quantum Transform Theory in Bargmann–Fock Space and Its Preliminary Application*

Abstract: A general theory for the linear transform in Bargmann–Fock space of n-mode boson system is presented. The group structure of transform is analyzed and the explicit expressions of transform operations in terms of normal ordering are given. As applications, a series of useful identities are given, the decoupling problem for general two-boson interaction and the normal product calculation of boson exponential quadratic operators are studied.

Reciprocal-wedge transform: a space-variant image representation

Abstract: The problems in computer vision have traditionally been approached as recovery problems. In active vision, perception is viewed as an active process of exploratory, probing and searching activities rather than a passive re-construction of the physical world. To facilitate effective interaction with the environment, a foveate sensor coupled with fast and precise gaze control mechanism becomes essential for active data acquisition. In this thesis, the Reciprocal-Wedge Transform (RWT) is proposed as a spacevariant image model. The RWT has its merits in comparison with other alternative foveate sensing models such as the log-polar transform. The concise matrix representation makes it enviable for its simplified computation procedures. Similar to the log-polar transform, the RWT facilitates space-variant sensing which enables effective use of variable-resolution data and the reduction of the total amount of the sensory data. Most interestingly, its property of anisotropic mapping yields variable resolution primarily in one dimension. Consequently, the RWT preserves linear features and performs especially well on translations in the images. A projective model is developed for the transform, lending it to potential hardware implementation of RWT projection cameras. The CCD camera for the log-polar transform requires sensing elements of exponentially varying sizes. In contrast, the RWT camera achieves variable resolution with oblique image plane projection, thus alleviating the need for non-rectangular tessellation and sensitivity scaling on the sensing elements. A camera model making use of the available lens design techniques is investigated. The RWT is applied to motion analysis and active stereo to illustrate the effectiveness of the image model. In motion analysis, two types of motion stereo are investigated, namely, longitudinal and lateral motion stereo. RWT motion stereo algorithms are developed for linear and circular ego motions in road navigation, and depth recovery from moving parts on an assembly belt. The algorithms benefit from the perspective correction, linear feature preservation and efficient data reduction of the RWT. The RWT imaging model is also shown to be suitable for fixation control in active stereo. Vergence and versional eye movements and scanpath behaviors are studied. A computational interpretation of stereo fusion in relation to disparity limit in spacevariant imagery leads to the development of a computational model for binocular fixation. The unique oculomotor movements for binocular fixation observed in human system appears natural to space-variant sensing. The vergence-version movement sequence is implemented for an effective fixation mechanism in RWT imaging. An interactive fixation system is simulated to show the various modules of camera control, vergence and version. Compared to the traditional reconstructionist approach, active behavior is shown to be plausible.

Three-dimensional object tracking using a Fourier transform of sine-coded range images

Abstract: An efficient method for tracking the attitude and translation of an object from a sequence of dense range images is demonstrated. The range data are sine coded and then Fourier transformed. By this process, planar surfaces in the image produce distinctive peaks in the Fourier transform spectrum. The position of a peak provides a direct measure of the normal of the plane. Tracking the positions of these peaks enables tracking the orientation of a known object. After computing and undoing the rotation, the translation is obtained by measuring the 3-D centroid of the segmented planar surfaces. All computations are closed form. The Fourier transform method is also used for segmentation. The integrative nature of the Fourier transform is very effective in attenuating the effect of noise and outliers. Results of tracking an object in a simulated range image sequence show high accuracy [0.2 deg in orientation and 0.2% root-mean-square (rms) error in translation with respect to the width of the object]. The system runs presently at 3 to 5 frames/s. The method promises real-time (video rate) performance with the addition of accelerator hardware for computing the Fourier transform. The approach is well suited for dynamic robotic vision applications.

The $p$-Product and its Applications in Signal Processing

Abstract: This paper introduces a new matrix product that proves useful in the representation of a large class of orthogonal transforms. It is shown that transform representation in terms of this product provides novel computational methods for computing the fast Fourier transform, the fast Walsh transform, a fast generalized Walsh transform, as well as a fast wavelet transform. Uniqueness and the advantages of this new formalism over traditional methods are also discussed.

Very-low-bit-rate coding of image sequences using the Gabor transform

Abstract: — While the need for image-sequence compression has long been understood, recent applications have shown that existing methods are not always sufficient. A case in point is the class of applications referred to as “very low bit rate.” These applications require the transmission of sequences over very narrow channels, e.g., 9600 bits/s. The compression ratios required are substantially beyond those that can be accomplished (with reasonable image quality) using standard methods. The Gabor transform is a local frequency decomposition which has been proposed as a model of the early stages of human vision. It has found widespread use for a number of tasks in signal and image processing, including image compression. In this paper, we examine Gabor transform-based coding for image-sequence transmission at rates near 10 kbits/s.

Haar wavelet transform with interband prediction and its application to image coding

Abstract: Although the discrete cosine transform (DCT) and wavelet transform have been used as effective techniques for reducing the redundancy of image waveforms, they have the problems of high complexity and causing block distortion. In this paper, a Haar wavelet transform with interband prediction is proposed that permits high-speed processing and which is suitable for coding as a subband decomposition technique since it generates little block distortion in the decoded images. the interband prediction method of this proposed transform method uses the derivative of the low-band waveform to predict the high-band waveform each time a band is split into two sub-bands. This results in a transform process that gives a prediction residual signal with lower entropy. During the inverse transform, the prediction coefficients obtained from the forward transform are used to predict the high-frequency waveforms and then, by adding the prediction residual, the original high frequency waveforms are reconstructed. Because the high-frequency waveforms are generated that smoothly interpolate the up-sampled, low-frequency waveforms, any block effects from this prediction technique are difficult to see in the decoded image. A detailed analysis of the proposed interband prediction process is performed by interpreting the proposed transform as a subband decomposition process that is based on the use of a symmetric short-kernel filter (SSKF) filter bank; then experiments are conducted that demonstrate its performance as a subband decomposition for coding of real image data and the possibility of progressive build-up of the decoded images. Results show that this transform method is effective for coding image data.