Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets

Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G.

doi:10.1109/tip.2008.924282

Cited by 109 publications

(15 citation statements)

References 40 publications

(96 reference statements)

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“…The quaternion theory [84] and multilinear algebra theory [85] developed in recent years are very suitable for processing high-dimensional vector signals, and they have been successfully applied in the fields of electromagnetic physics [86], multi-channel digital communication [87], and color image processing [88,89]. Therefore, it will be of significant interest to study more sophisticated and systematic methods of multi-component seismic vector field processing based on the quaternion or multilinear algebra theory, thereby exploiting the potential capability of multi-component seismic data in solving the problem of complex anisotropic media.…”

Section: Suggestionmentioning

confidence: 99%

Discussions on the Processing of the Multi-Component Seismic Vector Field

Wang

Sun

et al. 2019

Applied Sciences

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Multi-component seismic data contain a great deal of vector field information that reflects the situation of the underground medium. However, the processing methods used for multi-component seismic data are still being developed, and effectively retaining and using this information is the difficulty and the focus of the task. Currently, the main-stream processing techniques of multi-component seismic data treat the individual components independently as a scalar field; in this way, they do not excavate the vector features of the wavefield, thus restricting the potential utilities of the effective information. Research into processing methods that are suitable for use with the vector field, which can better retain and use the orientations and the relative amplitude relationship between multi-component seismic data, is urgently needed and represent an important direction for the current development of multi-component seismic data processing techniques. In this paper, we introduce and summarize several existing vector pre-processing techniques, including polarization filtering, de-noising using vector order statistics, group sparse representation, and vector separation of compressional waves and shear waves, to help scholars develop more effective vector field processing methods and to promote the development of vector processing techniques for multi-component seismic data.

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Section: Suggestionmentioning

confidence: 99%

Discussions on the Processing of the Multi-Component Seismic Vector Field

Wang

Sun

et al. 2019

Applied Sciences

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“…Peng and Zhao (2004) succeeded in designing three symmetric quaternion scaling filters but as shown by Ginzberg (2013, pp. 130/1), these filters were in fact trivial, meaning that they could be decomposed into independent complex Table 1: Summary of research by application which has used the QWT formulation of Chan et al (2008).…”

Section: The Dual Tree Quaternion Wavelet Transformmentioning

confidence: 99%

The development of the quaternion wavelet transform

Fletcher

Sangwine

2017

Signal Processing

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The development of the quaternion wavelet transform, Signal Processing, http://dx.doi.org/10. 1016/j.sigpro.2016.12.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the "QWTs" we have described do not fit our definition.

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“…Chan and his co-authors also developed a multiscale flow/motion estimation algorithm that computes a disparity flow map between two images with respect to local object motion [32]. Soulard and Carré have developed an efficient method for texture classification, thanks to coherent multiscale analysis brought by the magnitude and phase of the quaternionic wavelet transform [13].…”

Section: Phase Regularizationmentioning

confidence: 99%

Magnitude-phase of the dual-tree quaternionic wavelet transform for multispectral satellite image denoising

2014

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In this paper, we study the potential of the quaternionic wavelet transform for the analysis and processing of multispectral images with strong structural information. This new representation gives a very good division of the coefficients in terms of magnitude and three-phase angles and generalizes better the concept of analytic signal to image. Furthermore, it retains the property of shift invariant and directivity. We show an application of this transform in satellite image denoising. The proposed approach relies on the adaptation of thresholding procedures based on the dependency between magnitude quaternionic coefficients in local neighborhoods and phase regularization. In addition a non-marginal aspect of multispectral representation is introduced. Thanks to coherent analysis provided by the quaternionic wavelet transformation, the results obtained indicate the potential of this multispectral representation with magnitude thresholding and phase smoothing in noise reduction and edge preservation compared with classical wavelet thresholding methods that do not use phase or multiband information.

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Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets

Cited by 109 publications

References 40 publications

Discussions on the Processing of the Multi-Component Seismic Vector Field

Discussions on the Processing of the Multi-Component Seismic Vector Field

The development of the quaternion wavelet transform

Magnitude-phase of the dual-tree quaternionic wavelet transform for multispectral satellite image denoising

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