Analyzing laser plasma interferograms with a continuous wavelet transform ridge extraction technique: the method

Laser plasma interferograms are currently analyzed by extraction of the phase-shift map with fast Fourier transform (FFT) techniques [Appl. Opt. 18, 3101 (1985)]. This methodology works well when interferograms are only marginally affected by noise and reduction of fringe visibility, but it can fail to produce accurate phase-shift maps when low-quality images are dealt with. We present a novel procedure for a phase-shift map computation that makes extensive use of the ridge extraction in the continuous wavelet transform (CWT) framework. The CWT tool is flexible because of the wide adaptability of the analyzing basis, and it can be accurate because of the intrinsic noise reduction in the ridge extraction. A comparative analysis of the accuracy performances of them new tool and the FFT-based one shows that the CWT-based tool produces phase maps considerably less noisy and that it can better resolve local inhomogeneties. (C) 2001 Optical Society of America.

Enhanced approach for latent semantic indexing using wavelet transform

Latent semantic indexing (LSI) is a technique used for intelligent information retrieval (IR). It can be used as an alternative to traditional keyword matching IR and is attractive in this respect because of its ability to overcome problems with synonymy and polysemy. This study investigates various aspects of LSI: the effect of the Haar wavelet transform (HWT) as a preprocessing step for the singular value decomposition (SVD) in the key stage of the LSI process; and the effect of different threshold types in the HWT on the search results. The developed method allows the visualisation and processing of the term document matrix, generated in the LSI process, using HWT. The results have shown that precision can be increased by applying the HWT as a preprocessing step, with better results for hard thresholding than soft thresholding, whereas standard SVD-based LSI remains the most effective way of searching in terms of recall value.

Wavelet analysis of bender element signals

Accurate determination of shear wave arrival time using bender elements may be severely affected by a combination of near-field effects and reflected waves. These may mask the first arrival of the shear wave, making its detection difficult in the time domain. This paper describes an approach for measuring the shear wave arrival time through analysis of the output signal in the time-scale domain using a multi-scale wavelet transform. The local maxima lines of the wavelet transform modulus are observed at different scales, and all singularities are mathematically characterised, allowing subsequent detection of the singularity relating to the first arrival. Examples of the use of this approach on typical synthetic and experimental bender element signals are also supplied, and these results are compared with those from other time and frequency domain approaches. The wavelet approach is not affected by near-field effects, but instead is characterised by a relatively consistent singularity related to the shear wave arrival time, across a range of frequencies and noise levels.

A wavelet-based damage detection algorithm based on bridge acceleration response to a vehicle

Previous research based on theoretical simulations has shown the potential of the wavelet transform to detect damage in a beam by analysing the time-deflection response due to a constant moving load. However, its application to identify damage from the response of a bridge to a vehicle raises a number of questions. Firstly, it may be difficult to record the difference in the deflection signal between a healthy and a slightly damaged structure to the required level of accuracy and high scanning frequencies in the field. Secondly, the bridge is going to have a road profile and it will be loaded by a sprung vehicle and time-varying forces rather than a constant load. Therefore, an algorithm based on a plot of wavelet coefficients versus time to detect damage (a singularity in the plot) appears to be very sensitive to noise. This paper addresses these questions by: (a) using the acceleration signal, instead of the deflection signal, (b) employing a vehicle-bridge finite element interaction model, and (c) developing a novel wavelet-based approach using wavelet energy content at each bridge section which proves to be more sensitive to damage than a wavelet coefficient line plot at a given scale as employed by others.

Rapid design of discrete orthonormal wavelet transforms

A methodology which allows a non-specialist to rapidly design silicon wavelet transform cores has been developed. This methodology is based on a generic architecture utilizing time-interleaved coefficients for the wavelet transform filters. The architecture is scaleable and it has been parameterized in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is designed in such a way that the cores can also be cascaded without any interface glue logic for any desired level of decomposition. This parameterization allows the use of any orthonormal wavelet family thereby extending the design space for improved transformation from algorithm to silicon. Case studies for stand alone and cascaded silicon cores for single and multi-stage analysis respectively are reported. The typical design time to produce silicon layout of a wavelet based system has been reduced by an order of magnitude. The cores are comparable in area and performance to hand-crafted designs. The designs have been captured in VHDL so they are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Design and implementation of the symmetrically extended 2-D wavelet transform

The inclusion of the Discrete Wavelet Transform in the JPEG-2000 standard has added impetus to the research of hardware architectures for the two-dimensional wavelet transform. In this paper, a VLSI architecture for performing the symmetrically extended two-dimensional transform is presented. This architecture conforms to the JPEG-2000 standard and is capable of near-optimal performance when dealing with the image boundaries. The architecture also achieves efficient processor utilization. Implementation results based on a Xilinx Virtex-2 FPGA device are included.

Rapid silicon design of discrete orthonormal wavelet transforms based algorithms

A methodology has been developed which allows a non-specialist to rapidly design silicon wavelet transform cores for a variety of specifications. The cores include both forward and inverse orthonormal wavelet transforms. This methodology is based on efficient, modular and scaleable architectures utilising time-interleaved coefficients for the wavelet transform filters. The cores are parameterized in terms of wavelet type and data and coefficient word lengths. The designs have been captured in VHDL and are hence portable across a range of silicon foundries as well as FPGA and PLD implementations.

Rapid VLSI design of biorthogonal wavelet transform cores

A rapid design methodology for biorthogonal wavelet transform cores has been developed. This methodology is based on a generic, scaleable architecture for the wavelet filters. The architecture offers efficient hardware utilization by combining the linear phase property of biorthogonal filters with decimation in a MAC based implementation. The design has been captured in VHDL and parameterized in terms of wavelet type, data word length and coefficient word length. The control circuit is embedded within the cores and allows them to be cascaded without any interface glue logic for any desired level of decomposition. The design time to produce silicon layout of a biorthogonal wavelet based system is typically less than a day. The resulting silicon cores produced are comparable in area and performance to hand-crafted designs. The designs are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Wavelet packet transforms for system-on-chip applications

A methodology for the production of silicon cores for wavelet packet decomposition has been developed. The scheme utilizes efficient scalable architectures for both orthonormal and biorthogonal wavelet transforms. The cores produced from these architectures can be readily scaled for any wavelet function and are easily configurable for any subband structure. The cores are fully parameterized in terms of wavelet choice and appropriate wordlengths. Designs produced are portable across a range of silicon foundries as well as FPGA and PLD technologies. A number of exemplar implementations have been produced.

Comparison of Wavelet Transform and Time-Domain Analysis of Second Trimester Uterine Artery Doppler Waveforms in Screening for Pre-Eclampsia

The aim of this study was to compare time-domain waveform analysis of second-trimester uterine artery Doppler using the resistance index (RI) with waveform analysis using a mathematical tool known as wavelet transform for the prediction of pre-eclampsia (PE). This was a retrospective, nested case-cohort study of 336 women, 37 of whom subsequently developed PE. Uterine artery Doppler waveforms were analysed using both RI and waveform analysis. The utility of these indices in screening for PE was then evaluated using receiver operating characteristic curves. There were significant differences in uterine artery RI between the PE women and those with normal pregnancy outcome. After wavelet analysis, significant difference in the mean amplitude in wavelet frequency band 4 was noted between the 2 groups. The sensitivity for both Doppler RI and frequency band 4 for the detection of PE at a 10% false-positive rate was 45%. This small study demonstrates the application of wavelet transform analysis of uterine artery Doppler waveforms in screening for PE. Further prospective studies are needed in order to clearly define if this analytical approach to waveform analysis may have the potential to improve the detection of PE by uterine artery Doppler screening.