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.

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.

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.

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.

A Kind of DWT Domain Image Digital Watermarking Algorithm Research

2014 ◽  
Vol 1044-1045 ◽  
pp. 991-994
Author(s):  
Tao Liu
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Digital Watermarking ◽  
Wavelet Decomposition ◽  
Low Frequency ◽  
Discrete Wavelet ◽  
Original Image ◽  
Adaptive Watermarking ◽  
Frequency Domain Methods

An image-adaptive watermarking algorithm based on wavelet transform was proposed. At first, A digital image used as watermarking was scrambled. Next, the original image was decomposed by discrete wavelet transform,and in accordance with the characteristics of human visual system, wavelet decomposition in the low-frequency domain, Methods which average of adjacent domain instead of single wavelet decomposition coefficients was used to estimate and quantitative, watermarking was adaptively embedded in wavelet coefficients of low-frequency domain. At last, the simulation experimental results show that the algorithm for a variety of conventional image processing has good robustness.

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.

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