Showing papers on "Harmonic wavelet transform published in 1995"

Translation-Invariant De-Noising

Abstract: De-Noising with the traditional (orthogonal, maximally-decimated) wavelet transform sometimes exhibits visual artifacts; we attribute some of these—for example, Gibbs phenomena in the neighborhood of discontinuities—to the lack of translation invariance of the wavelet basis. One method to suppress such artifacts, termed “cycle spinning” by Coifman, is to “average out” the translation dependence. For a range of shifts, one shifts the data (right or left as the case may be), De-Noises the shifted data, and then unshifts the de-noised data. Doing this for each of a range of shifts, and averaging the several results so obtained, produces a reconstruction subject to far weaker Gibbs phenomena than thresholding based De-Noising using the traditional orthogonal wavelet transform.

Texture classification and segmentation using wavelet frames

Abstract: This paper describes a new approach to the characterization of texture properties at multiple scales using the wavelet transform. The analysis uses an overcomplete wavelet decomposition, which yields a description that is translation invariant. It is shown that this representation constitutes a tight frame of l/sub 2/ and that it has a fast iterative algorithm. A texture is characterized by a set of channel variances estimated at the output of the corresponding filter bank. Classification experiments with l/sub 2/ Brodatz textures indicate that the discrete wavelet frame (DWF) approach is superior to a standard (critically sampled) wavelet transform feature extraction. These results also suggest that this approach should perform better than most traditional single resolution techniques (co-occurrences, local linear transform, and the like). A detailed comparison of the classification performance of various orthogonal and biorthogonal wavelet transforms is also provided. Finally, the DWF feature extraction technique is incorporated into a simple multicomponent texture segmentation algorithm, and some illustrative examples are presented. >

The Stationary Wavelet Transform and some Statistical Applications

Abstract: Wavelets are of wide potential use in statistical contexts. The basics of the discrete wavelet transform are reviewed using a filter notation that is useful subsequently in the paper. A ‘stationary wavelet transform’, where the coefficient sequences are not decimated at each stage, is described. Two different approaches to the construction of an inverse of the stationary wavelet transform are set out. The application of the stationary wavelet transform as an exploratory statistical method is discussed, together with its potential use in nonparametric regression. A method of local spectral density estimation is developed. This involves extensions to the wavelet context of standard time series ideas such as the periodogram and spectrum. The technique is illustrated by its application to data sets from astronomy and veterinary anatomy.

Frequency‐time decomposition of seismic data using wavelet‐based methods

Abstract: Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency-time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time-frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale-translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive-source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet-based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform

Abstract: A new approach is presented for investigating the dispersive character of structural waves. The wavelet transform is applied to the time-frequency analysis of dispersive waves. The flexural wave induced in a beam by lateral impact is considered. It is shown that the wavelet transform using the Gabor wavelet effectively decomposes the strain response into its time-frequency components. In addition, the peaks of the time-frequency distribution indicate the arrival times of waves. By utilizing this fact, the dispersion relation of the group velocity can be accurately identified for a wide range of frequencies.

Wavelet spectra compared to Fourier spectra

Abstract: The relation between Fourier spectra and spectra obtained from wavelet analysis is established. Small scale asymptotic analysis shows that the wavelet spectrum is meaningful only when the analyzing wavelet has enough vanishing moments. These results are related to regularity theorems in Besov spaces. For the analysis of infinitely regular signals, a new wavelet, with an infinite number of cancellations is proposed.

Resolution enhancement of images using wavelet transform extrema extrapolation

Abstract: One problem of image interpolation refers to magnifying a small image without loss in image clarity. We propose a wavelet based method which estimates the higher resolution information needed to sharpen the image. This method extrapolates the wavelet transform of the higher resolution based on the evolution of the wavelet transform extrema across the scales. By identifying three constraints that the higher resolution information needs to obey, we enhance the reconstructed image through alternating projections onto the sets defined by these constraints.

Nonlinear processing of a shift-invariant discrete wavelet transform (DWT) for noise reduction

Abstract: A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in somewavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of theusual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelettransform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach,both in terms of the 12 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.Keywords: noise reduction, shift invariance, redundancy, wavelet transform, SAR 1 INTRODUCTION Recently a novel approach for noise reduction due to Donoho and Johnstone'2"3 has been established. It employs thresholding in the wavelet domain and can be shown to be asymptotically near optimal for a wide class

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

Fast Wavelet Based Volume Rendering by Accumulation of Transparent Texture Maps

Abstract: In the following paper, a new method for fast and accurate volume intensity and color integration is elaborated, which employs wavelet decompositions and texture mapping. At this point, it comprises and unifies the advantages of recently introduced Fourier domain volume rendering techniques and wavelet based volume rendering. Specifically, the method computes analytic solutions of the ray intensity integral through a single wavelet by slicing its Fourier transform and by backprojecting it into the spatial domain. The resulting slices can be considered as RGB textures where R, G and B account for the decomposed volume color function. Due to the similarity of the basis functions, the computation of the texture map has to be figured out only once for each 3D mother wavelet. Hence, the final volume rendering procedure turns out to be a superposition of self-similar, transparent and colored textures, which is supported by modern hardware accumulation buffers. Linear shading and attenuation can be introduced by modifications of the wavelet's Fourier transform.

Image Analysis of Mispicks in Woven Fabric

Abstract: Images of a woven fabric with missing picks are digitized, and three different image analysis techniques are compared: the Sobel edge operator, the fast Fourier transform, and the discrete wavelet transform. The wavelet transform, used as a multi-resolution spectral filter, is able to give both spectral and frequency information about a fabric. For the samples tested, the wavelet transform can characterize defects due to missing picks and ends faster and more accurately than the other methods.

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.

Registration and statistical analysis of PET images using the wavelet transform

Abstract: We have described a general procedure for the processing and analysis of PET data. We have used the multiresolution framework of the wavelet transform to derive new solutions for the two main processing steps. The first task was to align the various brain images using a general affine deformation model. Our registration procedure uses a continuous polynomial spline image model and takes advantage of the multiresolution structure of the underlying function spaces. This method implements a nonlinear least squares optimization technique with a coarse-to-fine iteration strategy that substantially improves the overall performance of the algorithm. The second task was to analyze the series of registered images and to detect the between group differences in metabolic brain activity. We chose to take advantage of the orthogonality and localization properties of the wavelet transform. Our approach was to apply this transform to the group-difference image and identify the wavelet channels that are globally significantly different from noise. >

New signal representation based on the fractional Fourier transform: definitions

Abstract: The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the application of various geometric operations on this new chart, such as radial and angular shearing and rotation, optical systems may be designed or analyzed. The field distribution, as well as full information about the spectrum and the space–bandwidth product, can be easily obtained in all the stages of the optical system.

Theory and applications of the shift-invariant, time-varying and undecimated wavelet transforms

Abstract: In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shift-invariant, time-varying, undecimated, and signal dependent. The result is a set of powerful and eecient algorithms suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection. These algorithms are comparable and often superior to traditional methods. In this sense, we put wavelets in action. Acknowledgments I want to thank my thesis advisor, Dr. Sidney Burrus, for introducing me into the theory of wavelets, and for his encouragement and guidance. His perspective and insight had a profound innuence on this thesis. I also would like to thank the members of my thesis committee, Dr. Richard Baraniuk and Dr. Ronny Wells. They all provided substantial input throughout the period during which this research was being done. I am also indebted to Ramesh Gopinath for his help and encouragement. Thanks to the members of the DSP group and the Computational Mathematic Laboratory of Rice University for many fruitful discussions and collaborations. Special thanks to Odegard of the DSP group for reading earlier drafts of this thesis. The generous nancial support of ARPA and Texas ATP grant that made this research possible is also gratefully acknowledged. Also, I would like to thank all those authors who made their technical reports and publications readily available on the Internet and the World Wide Web. On the personal side, I would like to thank my parents for making this all possible through their constant support and understanding over the years. I really appreciate the love and support of my companion, Lin Yue, who has been exploring life with me and shares my interest in academic endeavor.

Reconstruction of inverse synthetic aperture radar image using adaptive time-frequency wavelet transform

Abstract: Inverse synthetic aperture radar (ISAR) uses target's motion to generate images on the range- Doppler plane. The conventional ISAR uses Fourier transform to compute Doppler spectrum for each range cell. Due to the target irregular translational and rotational motion, the Doppler frequency in fact is time-varying. By using Fourier transform, the reconstructed image becomes blurred. To represent time-varying Doppler spectrum, time-frequency transform should be utilized. Adaptive time-frequency wavelet transform is a very useful tool in analysis of signals with time-varying spectrum. We applied adaptive time-frequency wavelet transform to ISAR image reconstruction and developed a simulation procedure to describe the characteristics of the algorithm. By replacing the conventional Fourier processor with the adaptive wavelet processor, a 2-D range-Doppler Fourier ISAR frame becomes a 3-D time- range-Doppler wavelet ISAR cube. By sampling in time, a time sequence of 2-D range- Doppler images can be viewed. Each individual wavelet ISAR image provides not only superior resolution but also the temporal information within each frame time. Both simulated and real ISAR data have been tested. The result from simulated ISAR data is illustrated in this paper.

On the continuous wavelet transform of second-order random processes

Abstract: Some second-order properties of random processes such as periodic correlation, stationarity, harmonizability, self-similarity, are characterized via corresponding properties of their wavelet transform: any one of these properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. These results are then specialized to fractional Brownian motion and other self-similar processes. >

Joint wavelet-transform correlator for image feature extraction

Abstract: We describe a joint wavelet-transform correlator in which the wavelet function is combined with the input image as the input joint image to realize the wavelet transform of the objective image. The Haar wavelet and the Roberts filter are chosen as the wavelet functions to extract the features of the objective image. The relationship of the Haar wavelet and the Roberts filter is analyzed mathematically based on admissible condition of the wavelet. Computer simulations are provided to verify the theory and to illustrate the performance of this correlator.

Two-dimensional wavelet transform achieved by computer-generated multireference matched filter and Dammann grating

Abstract: A two-dimensional wavelet transform is optically performed in real time by use of a new multichannel system that processes the different daughter wavelets separately. The system, which is able to handle every wavelet function, relies on a Dammann grating for generating a multichannel array. All channels are processed in parallel by a conventional two-dimensional correlator. Experimental results applying Morlet-wavelet decomposition are presented.

Wavelets as alternative to short-time Fourier transform in signal-averaged electrocardiography.

Abstract: The paper reports experience of using the wavelet transform to build time-frequency distributions of the terminal portion of the QRS-complex. We used wavelets of Morlet at 12 scales, grouped in three sets, to analyse the frequency range 33–404 Hz. On the same patient data we applied the short-time Fourier transform and compared the results. Both representations reflected the time-frequency contents and detected irregular structures in the terminal portion of the QRS complex. The wavelet transform revealed more adequately QRS prolongations characteristic of patients prone to ventricular tachycardia. We may conclude that the wavelet transform can be a flexible alternative to short-time Fourier transform.

Wavelet transform signal processing for dispersion analysis of ultrasonic signals

Abstract: The wavelet transform provides a new tool for analyzing the time-frequency evolution of transient signals as an alternative to the classical short-time Fourier transform. The purpose of the present paper is to provide an overview of the applicability of the wavelet transform technique to the analysis of the propagation of dispersive ultrasonic waves. The wavelet transform is briefly introduced, with special emphasis on the relationship between the wavelet transform and the group velocity of dispersed signals. A complex mother wavelet is utilized to obtain the time evolution of the various spectral components of the ultrasonic signal, and the magnitude of the wavelet transform is used to represent the envelope of the ultrasonic pulse and to determine the time of arrival of the acoustic energy. This approach results in a time-scale representation of the ultrasonic signal which is extremely useful in the characterization of thin coatings using the dispersion behavior of the surface wave velocity. The technique was applied for the measurement of elastic constants of chromium coatings on steel substrates using laser-generated surface acoustic waves. Numerical simulations and experimental results are presented to discuss the usefulness of the wavelet transform.