Multiwavelets

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A.e. Bell - One of the best experts on this subject based on the ideXlab platform.

  • Color image compression: Multiwavelets vs. scalar wavelets
    2002 IEEE International Conference on Acoustics Speech and Signal Processing, 2002
    Co-Authors: S. Rout, A.e. Bell
    Abstract:

    Recently developed balanced Multiwavelets have proven effective for image compression; however, their performance falls slightly short of the scalar wavelets. A previous comparison of some scalar wavelet and multi wavelet properties illustrated their importance for grayscale image compression. In this paper we present another property: the perfect reconstruction (PR) property; it too appears to explain the performance differences. This paper compares the compression performance of 3 scalar wavelets and 5 balanced Multiwavelets on 7 color images. We observe that SA4 depicts the best performance amongst the multi wavelets in terms of both subjective quality and PSNR; this matches our expectation based on our results that indicate that it is the only BMW which satisfies the PR conditions. Although SA4 rivals the biorthogonal scalar wavelets in terms of many desirable properties, it suffers from a lower balancing/vanishing order. This difference explains the 0.01–0.47 dB performance gap between the best scalar wavelet and the best balanced multiwavelet.

  • New image compression techniques using Multiwavelets and multiwavelet packets
    IEEE Transactions on Image Processing, 2001
    Co-Authors: M.b. Martin, A.e. Bell
    Abstract:

    Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry. However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of the desirable properties. The relatively new field of Multiwavelets shows promise in obviating some of the limitations of wavelets. Multiwavelets offer more design options and are able to combine several desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms. This paper presents new multiwavelet transform and quantization methods and introduces multiwavelet packets. Extensive experimental results demonstrate that our techniques exhibit performance equal to, or in several cases superior to, the current wavelet filters.

Lixin Shen - One of the best experts on this subject based on the ideXlab platform.

  • A general approach for analysis and application of discrete multiwavelet transforms
    IEEE Transactions on Signal Processing, 2000
    Co-Authors: Jo Yew Tham, Lixin Shen
    Abstract:

    This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet) filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good multifilter properties (GMPs), which define the desirable filter characteristics of the equivalent scalar filters. We then relate the notion of GMPs directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system. Second, we propose a generalized, efficient, and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post-synthesis multirate filtering techniques. Finally, our simulations verified that both orthogonal and biorthogonal Multiwavelets that possess GMPs and employ the proposed initialization technique can perform better than the popular scalar wavelets such as Daubechies'D8 wavelet and the D(9/7) wavelet, and some of these Multiwavelets achieved this with lower computational complexity.

  • new biorthogonal Multiwavelets for image compression
    Signal Processing, 1999
    Co-Authors: Lixin Shen, Jo Yew Tham
    Abstract:

    Abstract There has been a growing research interest in the areas of construction and application of Multiwavelets over the past few years. In a previous paper, we introduced a class of symmetric-antisymmetric orthonormal Multiwavelets which were constructed directly from orthonormal scalar wavelets. These Multiwavelets were shown to perform better than existing orthonormal Multiwavelets and scalar wavelets in terms of image compression performance and computational complexity. However, their performance still lags behind some popular biorthogonal scalar wavelets such as Daubechies’ D(9/7) and Villasenor's V(10/18). This paper aims to address this shortcoming by extending our earlier work to the biorthogonal setting. Two methods of construction are introduced; thus resulting in previously unpublished symmetric-antisymmetric biorthogonal multiwavelet filters. Extensive simulations showed that these multiwavelet filters can give an improvement of up to 0.7 dB over D(9/7) and V(10/18), and yet require only comparable but often lower computational cost. More importantly, better preservation of textures and edges of the reconstructed images was also observed.

  • A new multifilter design property for multiwavelet image compression
    1999 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), 1999
    Co-Authors: Jo Yew Tham, Lixin Shen
    Abstract:

    Approximation order, linear phase symmetry, time-frequency localization, regularity, and stopband attenuation are some criteria that are widely used in wavelet filter design. We propose a new criterion called good multifilter properties (GMPs) for the design and construction of multiwavelet filters targeting image compression applications. We first provide the definition of GMPs, followed by a necessary and sufficient condition for an orthonormal multiwavelet system to have a GMP order of at least 1. We then present an algorithm to construct orthogonal Multiwavelets possessing GMPs, starting from any length-2N scalar CQPs. Image compression experiments are performed to evaluate the importance of GMPs for image compression, as compared to other common filter design criteria. Our results confirmed that Multiwavelets that possess GMPs not only yield superior PSNR performances, but also require much lower computations in their transforms.

Jo Yew Tham - One of the best experts on this subject based on the ideXlab platform.

  • A general approach for analysis and application of discrete multiwavelet transforms
    IEEE Transactions on Signal Processing, 2000
    Co-Authors: Jo Yew Tham, Lixin Shen
    Abstract:

    This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet) filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good multifilter properties (GMPs), which define the desirable filter characteristics of the equivalent scalar filters. We then relate the notion of GMPs directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system. Second, we propose a generalized, efficient, and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post-synthesis multirate filtering techniques. Finally, our simulations verified that both orthogonal and biorthogonal Multiwavelets that possess GMPs and employ the proposed initialization technique can perform better than the popular scalar wavelets such as Daubechies'D8 wavelet and the D(9/7) wavelet, and some of these Multiwavelets achieved this with lower computational complexity.

  • new biorthogonal Multiwavelets for image compression
    Signal Processing, 1999
    Co-Authors: Lixin Shen, Jo Yew Tham
    Abstract:

    Abstract There has been a growing research interest in the areas of construction and application of Multiwavelets over the past few years. In a previous paper, we introduced a class of symmetric-antisymmetric orthonormal Multiwavelets which were constructed directly from orthonormal scalar wavelets. These Multiwavelets were shown to perform better than existing orthonormal Multiwavelets and scalar wavelets in terms of image compression performance and computational complexity. However, their performance still lags behind some popular biorthogonal scalar wavelets such as Daubechies’ D(9/7) and Villasenor's V(10/18). This paper aims to address this shortcoming by extending our earlier work to the biorthogonal setting. Two methods of construction are introduced; thus resulting in previously unpublished symmetric-antisymmetric biorthogonal multiwavelet filters. Extensive simulations showed that these multiwavelet filters can give an improvement of up to 0.7 dB over D(9/7) and V(10/18), and yet require only comparable but often lower computational cost. More importantly, better preservation of textures and edges of the reconstructed images was also observed.

  • A new multifilter design property for multiwavelet image compression
    1999 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), 1999
    Co-Authors: Jo Yew Tham, Lixin Shen
    Abstract:

    Approximation order, linear phase symmetry, time-frequency localization, regularity, and stopband attenuation are some criteria that are widely used in wavelet filter design. We propose a new criterion called good multifilter properties (GMPs) for the design and construction of multiwavelet filters targeting image compression applications. We first provide the definition of GMPs, followed by a necessary and sufficient condition for an orthonormal multiwavelet system to have a GMP order of at least 1. We then present an algorithm to construct orthogonal Multiwavelets possessing GMPs, starting from any length-2N scalar CQPs. Image compression experiments are performed to evaluate the importance of GMPs for image compression, as compared to other common filter design criteria. Our results confirmed that Multiwavelets that possess GMPs not only yield superior PSNR performances, but also require much lower computations in their transforms.

Zhengjia He - One of the best experts on this subject based on the ideXlab platform.

  • Multiwavelet transform and its applications in mechanical fault diagnosis - A review
    Mechanical Systems and Signal Processing, 2014
    Co-Authors: Hailiang Sun, Yanyang Zi, Jinglong Chen, Zhengjia He, Jing Yuan, Xiaodong Wang, Shuilong He
    Abstract:

    Mechanical fault diagnosis is important to reduce unscheduled machine downtime and avoid catastrophic accidents. It is significant to extract incipient fault and compound fault features as early as possible, which is a complex and challenging task that requests advanced analytical methods with high reliability, high accuracy and high efficiency. Compound fault features are mutually coupled in dynamic signals from the complex system. Weak features of incipient faults are always submersed in background noises. Multiwavelet transform is a remarkable development of wavelet transform, which uses vector scaling functions and wavelet functions. Multiwavelets possess the property of orthogonality, symmetry, compact support and high vanishing moments simultaneously. These advantages promote the development of Multiwavelets and their applications in mechanical fault diagnosis in the past decades. This paper attempts to summarize the recent development of multiwavelet transform and its applications in mechanical fault diagnosis. First, the history of wavelets and Multiwavelets is introduced. Second, the necessity and the overview of preprocessing methods for Multiwavelets are summarized. Third, the advantages of Multiwavelets and improvements of different generation Multiwavelets are addressed. Fourth, different algorithms of these multiwavelet transforms and their flow charts are presented. Fifth, engineering applications of Multiwavelets in mechanical fault diagnosis are investigated. This review also describes a simulation experiment and three application examples which provide a better understanding of different generation Multiwavelets for compound fault detection. Finally, existent problems and prospects of further researches are discussed. It is expected that this review will construct an image of the contributions of different generation Multiwavelets and link the current frontiers with engineering applications for readers interested in this field. © 2013 Elsevier Ltd. All rights reserved.

  • customized Multiwavelets for planetary gearbox fault detection based on vibration sensor signals
    Sensors, 2013
    Co-Authors: Yanyang Zi, Zhengjia He, Jing Yuan, Xiaodong Wang, Lue Chen
    Abstract:

    Planetary gearboxes exhibit complicated dynamic responses which are more difficult to detect in vibration signals than fixed-axis gear trains because of the special gear transmission structures. Diverse advanced methods have been developed for this challenging task to reduce or avoid unscheduled breakdown and catastrophic accidents. It is feasible to make fault features distinct by using multiwavelet denoising which depends on the feature separation and the threshold denoising. However, standard and fixed Multiwavelets are not suitable for accurate fault feature detections because they are usually independent of the measured signals. To overcome this drawback, a method to construct customized Multiwavelets based on the redundant symmetric lifting scheme is proposed in this paper. A novel indicator which combines kurtosis and entropy is applied to select the optimal Multiwavelets, because kurtosis is sensitive to sharp impulses and entropy is effective for periodic impulses. The improved neighboring coefficients method is introduced into multiwavelet denoising. The vibration signals of a planetary gearbox from a satellite communication antenna on a measurement ship are captured under various motor speeds. The results show the proposed method could accurately detect the incipient pitting faults on two neighboring teeth in the planetary gearbox.

  • the construction of finite element Multiwavelets for adaptive structural analysis
    International Journal for Numerical Methods in Biomedical Engineering, 2011
    Co-Authors: Youming Wang, Xuefeng Chen, Yumin He, Zhengjia He
    Abstract:

    A design method of finite element Multiwavelets is proposed for adaptive analysis of structural problems. A multiresolution analysis for Lagrange and Hermite finite element space is discussed. New classes of finite element Multiwavelets are constructed by the lifting scheme according to the operators of structural problems. Compared with classical wavelet methods, the finite element multiwavelet method is more flexible and robust for multiscale structural analysis. Based on the operator-orthogonality of the finite element Multiwavelets, we propose a new adaptive scheme for the finite element multiwavelet method by adding new Multiwavelets into the domain where the error estimator is larger than a given threshold value. Numerical examples demonstrate that the finite element Multiwavelets are flexible and are efficient bases in solving structural problems. Copyright © 2009 John Wiley & Sons, Ltd.

  • adaptive Multiwavelets via two scale similarity transforms for rotating machinery fault diagnosis
    Mechanical Systems and Signal Processing, 2009
    Co-Authors: Jing Yuan, Yanyang Zi, Zhengjia He, Zhen Li
    Abstract:

    Fault diagnosis of rotating machinery is very important and critical to avoid serious accidents. However, the complex and non-stationary vibration signals with a large amount of noise make the fault detection to be challenging, especially at the early stage. Based on the inner product principle, fault detection using wavelet transforms is to match fault features most correlative to basis functions, and its effectiveness is determined by the construction and choice of wavelet basis function. In this paper, a new method based on adaptive Multiwavelets via two-scale similarity transforms (TSTs) is proposed. Multiwavelets can offer multiple wavelet basis functions and so have the possibility of matching various fault features preferably. TSTs are simple and straightforward methods to design a series of new biorthogonal Multiwavelets with some desirable properties. Using TSTs, a changeable and adaptive multiwavelet library is established so as to provide various ascendant multiple basis functions for inner product operation. By the rule of kurtosis maximization principle, optimal Multiwavelets most similar to the fault features of a given signal are searched for. The applications to a rolling bearing of outer-race fault and a flue gas turbine unit of rub-impact fault show that the proposed method is an effective approach to detecting the impulse feature components hidden in vibration signals and performs well for rotating machinery fault diagnosis.

Jing Yuan - One of the best experts on this subject based on the ideXlab platform.

  • Multiwavelet transform and its applications in mechanical fault diagnosis - A review
    Mechanical Systems and Signal Processing, 2014
    Co-Authors: Hailiang Sun, Yanyang Zi, Jinglong Chen, Zhengjia He, Jing Yuan, Xiaodong Wang, Shuilong He
    Abstract:

    Mechanical fault diagnosis is important to reduce unscheduled machine downtime and avoid catastrophic accidents. It is significant to extract incipient fault and compound fault features as early as possible, which is a complex and challenging task that requests advanced analytical methods with high reliability, high accuracy and high efficiency. Compound fault features are mutually coupled in dynamic signals from the complex system. Weak features of incipient faults are always submersed in background noises. Multiwavelet transform is a remarkable development of wavelet transform, which uses vector scaling functions and wavelet functions. Multiwavelets possess the property of orthogonality, symmetry, compact support and high vanishing moments simultaneously. These advantages promote the development of Multiwavelets and their applications in mechanical fault diagnosis in the past decades. This paper attempts to summarize the recent development of multiwavelet transform and its applications in mechanical fault diagnosis. First, the history of wavelets and Multiwavelets is introduced. Second, the necessity and the overview of preprocessing methods for Multiwavelets are summarized. Third, the advantages of Multiwavelets and improvements of different generation Multiwavelets are addressed. Fourth, different algorithms of these multiwavelet transforms and their flow charts are presented. Fifth, engineering applications of Multiwavelets in mechanical fault diagnosis are investigated. This review also describes a simulation experiment and three application examples which provide a better understanding of different generation Multiwavelets for compound fault detection. Finally, existent problems and prospects of further researches are discussed. It is expected that this review will construct an image of the contributions of different generation Multiwavelets and link the current frontiers with engineering applications for readers interested in this field. © 2013 Elsevier Ltd. All rights reserved.

  • customized Multiwavelets for planetary gearbox fault detection based on vibration sensor signals
    Sensors, 2013
    Co-Authors: Yanyang Zi, Zhengjia He, Jing Yuan, Xiaodong Wang, Lue Chen
    Abstract:

    Planetary gearboxes exhibit complicated dynamic responses which are more difficult to detect in vibration signals than fixed-axis gear trains because of the special gear transmission structures. Diverse advanced methods have been developed for this challenging task to reduce or avoid unscheduled breakdown and catastrophic accidents. It is feasible to make fault features distinct by using multiwavelet denoising which depends on the feature separation and the threshold denoising. However, standard and fixed Multiwavelets are not suitable for accurate fault feature detections because they are usually independent of the measured signals. To overcome this drawback, a method to construct customized Multiwavelets based on the redundant symmetric lifting scheme is proposed in this paper. A novel indicator which combines kurtosis and entropy is applied to select the optimal Multiwavelets, because kurtosis is sensitive to sharp impulses and entropy is effective for periodic impulses. The improved neighboring coefficients method is introduced into multiwavelet denoising. The vibration signals of a planetary gearbox from a satellite communication antenna on a measurement ship are captured under various motor speeds. The results show the proposed method could accurately detect the incipient pitting faults on two neighboring teeth in the planetary gearbox.

  • adaptive Multiwavelets via two scale similarity transforms for rotating machinery fault diagnosis
    Mechanical Systems and Signal Processing, 2009
    Co-Authors: Jing Yuan, Yanyang Zi, Zhengjia He, Zhen Li
    Abstract:

    Fault diagnosis of rotating machinery is very important and critical to avoid serious accidents. However, the complex and non-stationary vibration signals with a large amount of noise make the fault detection to be challenging, especially at the early stage. Based on the inner product principle, fault detection using wavelet transforms is to match fault features most correlative to basis functions, and its effectiveness is determined by the construction and choice of wavelet basis function. In this paper, a new method based on adaptive Multiwavelets via two-scale similarity transforms (TSTs) is proposed. Multiwavelets can offer multiple wavelet basis functions and so have the possibility of matching various fault features preferably. TSTs are simple and straightforward methods to design a series of new biorthogonal Multiwavelets with some desirable properties. Using TSTs, a changeable and adaptive multiwavelet library is established so as to provide various ascendant multiple basis functions for inner product operation. By the rule of kurtosis maximization principle, optimal Multiwavelets most similar to the fault features of a given signal are searched for. The applications to a rolling bearing of outer-race fault and a flue gas turbine unit of rub-impact fault show that the proposed method is an effective approach to detecting the impulse feature components hidden in vibration signals and performs well for rotating machinery fault diagnosis.