Wavelet‐transform‐based prestack multiscale Kirchhoff migration

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1505-1512 ◽  
Author(s):  
Zhou Yu ◽  
George A. McMechan ◽  
Phil D. Anno ◽  
John F. Ferguson
Keyword(s):  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Computational Cost ◽  
Synthetic Data ◽  
Phase Distortion ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Kirchhoff Migration ◽  
Individual Scale ◽  
The Individual

We propose a Kirchhoff‐style algorithm that migrates coefficients obtained by wavelet decomposition of seismic traces over time. Wavelet‐based prestack multiscale Kirchhoff migration involves four steps: wavelet decomposition of the seismic data, thresholding of the resulting wavelet coefficients, multiscale Kirchhoff migration, and image reconstruction from the multiscale images. The migration procedure applied to each wavelet scale is the same as conventional Kirchhoff migration but operates on wavelet coefficients. Since only the wavelet coefficients are migrated, the cost of wavelet‐based migration is reduced compared to that of conventional Kirchhoff migration. Kirchhoff migration of wavelet‐decomposed data, followed by wavelet reconstruction, is kinematically equivalent to and yields similar migrated signal shapes and amplitudes as conventional Kirchhoff migration when data at all wavelet scales are included. The decimation in the conventional discrete pyramid wavelet decomposition introduces a translation‐variant phase distortion in the wavelet domain. This phase distortion is overcome by using a stationary wavelet‐transform rather than the conventional discrete wavelet‐transform of the data to be migrated. A wavelet reconstruction operator produces a single composite broadband migrated space‐domain image from multiscale images. Multiscale images correspond to responses in different frequency windows, and migrating the data at each scale has a different cost. Migrating some, or only one, of the individual scale data sets considerably reduces the computational cost of the migration. Successful 2D tests are shown for migrations of synthetic data for a point‐diffractor model, a multilayer model, and the Marmousi model.

Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data

2012 ◽  
Vol 239-240 ◽  
pp. 1213-1218 ◽  
Author(s):  
Mehdi Shahbazian ◽  
Saeed Shahbazian
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Least Square ◽  
Multidimensional Case ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Sampled Data ◽  
Irregularly Sampled Data

The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

Improving the Computational Cost for Copied Region Detection in Forensic Images

2016 ◽  
Vol 2 (1) ◽  
pp. 55
Author(s):  
Tu Huynh-Kha ◽  
Thuong Le-Tien ◽  
Synh Ha ◽  
Khoa Huynh-Van
Keyword(s):  
Wavelet Transform ◽  
Euclidean Distance ◽  
Research Work ◽  
Computational Cost ◽  
Correlation Coefficients ◽  
Zernike Moments ◽  
Computational Time ◽  
Discrete Wavelet ◽  
Feature Vectors ◽  
Region Detection

This research work develops a new method to detect the forgery in image by combining the Wavelet transform and modified Zernike Moments (MZMs) in which the features are defined from more pixels than in traditional Zernike Moments. The tested image is firstly converted to grayscale and applied one level Discrete Wavelet Transform (DWT) to reduce the size of image by a half in both sides. The approximation sub-band (LL), which is used for processing, is then divided into overlapping blocks and modified Zernike moments are calculated in each block as feature vectors. More pixels are considered, more sufficient features are extracted. Lexicographical sorting and correlation coefficients computation on feature vectors are next steps to find the similar blocks. The purpose of applying DWT to reduce the dimension of the image before using Zernike moments with updated coefficients is to improve the computational time and increase exactness in detection. Copied or duplicated parts will be detected as traces of copy-move forgery manipulation based on a threshold of correlation coefficients and confirmed exactly from the constraint of Euclidean distance. Comparisons results between proposed method and related ones prove the feasibility and efficiency of the proposed algorithm.

Efficient and Adaptive Rotation Invariant Wavelet Transform

2003 ◽  
Vol 01 (03) ◽  
pp. 353-372
Author(s):  
Chi-Man Pun
Keyword(s):  
Wavelet Transform ◽  
Texture Classification ◽  
Wavelet Packet ◽  
Sampling Rate ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Information Cost ◽  
Image Size ◽  
Rotation Invariant ◽  
Adaptive Wavelet

It is well known that the sensitivity to translations and orientations is a major drawback in 2D discrete wavelet transform (DWT). In this paper, we have proposed an effective scheme for rotation invariant adaptive wavelet packet transform. During decomposition, the wavelet coefficients are obtained by applying a polar transform (PT) followed by a row-shift invariant wavelet packet decomposition (RSIWPD). In the first stage, the polar transform generates a row-shifted image and is adaptive to the image size to achieve complete and minimum sampling rate. In the second stage, the RSIWPD is applied to the row-shifted image to generate rotation invariant but over completed subbands of wavelet coefficients. In order to reduce the redundancy and computational complexity, we adaptively select some subbands to decompose and form a best basis representation with minimal information cost with respect to an appropriate information cost function. With this best basis representation, the original image can be reconstructed easily by applying a row-shift invariant wavelet packet reconstruction (RSIWPR) followed by an inverse polar transform (IPT). In the experiments, we study the application of this representation for texture classification and achieve 96.5% classification accuracy.

scholarly journals Performance Analysis of Iris Recognition using Multi Stage Wavelet Transform Decomposition and Bicubic Interpolation Technique

2019 ◽  
Vol 8 (6) ◽  
pp. 1-10
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Iris Recognition ◽  
Image Features ◽  
Discrete Wavelet ◽  
Multi Stage ◽  
Human Iris ◽  
The Individual ◽  
Matching Score ◽  
Bicubic Interpolation

Biometric identification is highly reliable for human identification. Biometric is a field of science used for analyzing the physiological or behavioural characteristics of human. Iris features are unique, stable and can be visible from longer distances. It uses mathematical pattern-recognition techniques on video images of one or both iris of an individual's. Compared to other biometric traits, iris is more challenging and highly secured tool to identify the individual. In this paper iris recognition based on the combination of Discrete Wavelet Transform (DWT), Inverse Discrete Wavelet Transform (IDWT), Independent Component Analysis (ICA) and Binariezed Statistical Image Features (BSIF) are adopted to generate the hybrid iris features. The first level and second level DWT are employed in order to extract the more unique features of the iris images. The concept of bicubic interpolation is applied on high frequency coefficients generated by first level decomposition of DWT to produce new set of sub-bands. The approximation band generated by second level decomposition of DWT and new set of sub-bands produced by second level decomposition of DWT are applied on IDWT to reconstruct the coefficients. The ICA 5x5 filters and BSIF are adopted for selecting the appropriate images to extract the final features. Finally based on the matching score between the database image and test image the genuine and imposters are identified. Using CASIA database, training and testing of the features is performed and performance is evaluated considering different combinations of Person inside Database (PID) and Person outside Database (POD).

scholarly journals The Improvement of Discrete Wavelet Transform

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Wavelet Transform ◽  
Decay Rate ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Polynomial Interpolation ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Periodic Wavelet ◽  
Improved Algorithm

Discrete wavelet transform and discrete periodic wavelet transform have been widely used in image compression and data approximation. Due to discontinuity on the boundary of original data, the decay rate of the obtained wavelet coefficients is slow. In this study, we use the combination of polynomial interpolation and one-dimensional/two-dimensional discrete periodic wavelet transforms to mitigate boundary effects. The decay rate of the obtained wavelet coefficients in our improved algorithm is faster than that of traditional two-dimensional discrete wavelet transform. Moreover, our improved algorithm can be extended naturally to the higher-dimensional case.

Text Categorisation Through Dimensionality Reduction Using Wavelet Transform

2020 ◽  
Vol 19 (04) ◽  
pp. 2050039
Author(s):  
Jorge Chamorro-Padial ◽  
Rosa Rodríguez-Sánchez
Keyword(s):  
Wavelet Transform ◽  
Dimensionality Reduction ◽  
Text Classification ◽  
High Energy ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Vertical Orientation ◽  
Method Of Dimensionality Reduction ◽  
Horizontal Orientation ◽  
Relevant Level

This paper proposes a new method of dimensionality reduction when performing Text Classification, by applying the discrete wavelet transform to the document-term frequencies matrix. We analyse the features provided by the wavelet coefficients from the different orientations: (1) The high energy coefficients in the horizontal orientation correspond to relevant terms in a single document. (2) The high energy coefficients in the vertical orientation correspond to relevant terms for a single document, but not for the others. (3) The high energy coefficients in the diagonal orientation correspond to relevant terms in a document in comparison to other terms. If we filter using the wavelet coefficients and fulfil these three conditions simultaneously, we can obtain a reduced vocabulary of the corpus, with less dimensions than in the original one. To test the success of the reduced vocabulary, we recoded the corpus with the new reduced vocabulary and we obtained a statistically relevant level of accuracy for document classification.

MATHEMATICAL IMPLEMENTATION OF HYBRID FAST FOURIER TRANSFORM AND DISCRETE WAVELET TRANSFORM FOR DEVELOPING GRAPHICAL USER INTERFACE USING VISUAL BASIC FOR SIGNAL PROCESSING APPLICATIONS

2012 ◽  
Vol 12 (05) ◽  
pp. 1240031 ◽  
Author(s):  
MOUSA K. WALI ◽  
M. MURUGAPPAN ◽  
R. BADLISHAH AHMMAD
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Input Signal ◽  
Wavelet Decomposition ◽  
Wavelet Coefficient ◽  
Visual Basic ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
End User ◽  
Decomposition Level

In recent years, the application of discrete wavelet transform (DWT) on biosignal processing has made a significant impact on developing several applications. However, the existing user-friendly software based on graphical user interfaces (GUI) does not allow the freedom of saving the wavelet coefficients in .txt or .xls format and to analyze the frequency spectrum of wavelet coefficients at any desired wavelet decomposition level. This work describes the development of mathematical models for the implementation of DWT in a GUI environment. This proposed software based on GUI is developed under the visual basic (VB) platform. As a preliminary tool, the end user can perform "j" level of decomposition on a given input signal using the three most popular wavelet functions — Daubechies, Symlet, and Coiflet over "n" order. The end user can save the output of wavelet coefficients either in .txt or .xls file format for any further investigations. In addition, the users can gain insight into the most dominating frequency component of any given wavelet decomposition level through fast Fourier transform (FFT). This feature is highly essential in signal processing applications for the in-depth analysis on input signal components. Hence, this GUI has the hybrid features of FFT with DWT to derive the frequency spectrum of any level of wavelet coefficient. The novel feature of this software becomes more evident for any signal processing application. The proposed software is tested with three physiological signal — electroencephalogram (EEG), electrocardiogram (ECG), and electromyogram (EMG) — samples. Two statistical features such as mean and energy of wavelet coefficient are used as a performance measure for validating the proposed software over conventional software. The results of proposed software is compared and analyzed with MATLAB wavelet toolbox for performance verification. As a result, the proposed software gives the same results as the conventional toolbox and allows more freedom to the end user to investigate the input signal.

scholarly journals Sub-band selection approach to artifact suppression from electroencephalography signal using hybrid wavelet transform

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142199226
Author(s):  
Jannatul Ferdous ◽  
Sujan Ali ◽  
Ekramul Hamid ◽  
Khademul Islam Molla
Keyword(s):  
Wavelet Transform ◽  
Performance Metrics ◽  
Wavelet Packet ◽  
Reference Signal ◽  
Computational Cost ◽  
Discrete Wavelet ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Finite Set ◽  
Artifact Suppression

This article presents a hybrid wavelet-based algorithm to suppress the ocular artifacts from electroencephalography (EEG) signals. The hybrid wavelet transform (HWT) method is designed by the combination of discrete wavelet decomposition and wavelet packet transform. The artifact suppression is performed by the selection of sub-bands obtained by HWT. Fractional Gaussian noise (fGn) is used as the reference signal to select the sub-bands containing the artifacts. The multichannel EEG signal is decomposed HWT into a finite set of sub-bands. The energies of the sub-bands are compared to that of the fGn to the desired sub-band signals. The EEG signal is reconstructed by the selected sub-bands consisting of EEG. The experiments are conducted for both simulated and real EEG signals to study the performance of the proposed algorithm. The results are compared with recently developed algorithms of artifact suppression. It is found that the proposed method performs better than the methods compared in terms of performance metrics and computational cost.

scholarly journals Fuzzy Logic based Improvement in Discrete Wavelet Transform Edge Representation in Images.doc

2020 ◽  
Author(s):  
Anand Swaminathan
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Fuzzy Inference ◽  
Directional Derivative ◽  
Rule Base ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Inference System ◽  
Rule Structure

We introduce a rule base fuzzy technique on decomposed wavelet coefficients, to improve the wavelet edge representation. Our algorithm mitigates ‘incorrect’ responses, due primarily to the symmetries of directional derivative filters. Since the Discrete Wavelet Transform (DWT) coefficients are revealed from two dimensional symmetric filter banks and undermine some gradient information. These wavelet coefficients are prearranged into ‘if-then’ rule structure of a fuzzy inference system, to improve the wavelet edge representation.

scholarly journals Eliminated aliasing effect on wavelet transform based multiresolution analysis

2016 ◽  
Vol 55 (3) ◽  
Author(s):  
Ernesto González-Flores ◽  
José Oscar Campos-Enríquez ◽  
Erick Camacho-Ramírez ◽  
David Ernesto Rivera-Recillas
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multiresolution Analysis ◽  
Synthetic Data ◽  
Seismic Signal ◽  
Discrete Wavelet ◽  
Frequency Bands ◽  
Analysis Technique ◽  
The Time Domain ◽  
Seismic Signal Processing

Multiresolution analysis, based on the discrete wavelet transform, is here incorporated in seismic signal processing. This analysis technique enables decomposing a seismic signal, in different frequency bands, and thus to analyze the information contained in these frequency bands. Multiresolution analysis allows visualizing in the time domain the information contained in the frequency bands. Wavelets commonly used in the discrete wavelet transform present an overlay between scales, this constitutes an aliasing effect that gives rise to spurious effects. Vaidyanathan wavelet minimizes the overlay between scales. We applied this wavelet to synthetic data and to a 3D seismic cube. Accordingly, spurious effects from aliasing generated by overlay between scales are minimized with the Vaidyanathan wavelet.

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