The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Qingjiang Chen - One of the best experts on this subject based on the ideXlab platform.
-
characteristics of a class of vector valued non separable higher dimensional Wavelet packet bases
Chaos Solitons & Fractals, 2009Co-Authors: Qingjiang ChenAbstract:Abstract In this paper, we introduce vector-valued non-separable higher-dimensional Wavelet Packets with an arbitrary integer dilation factor. An approach for constructing vector-valued higher-dimensional Wavelet packet bases is proposed. Their characteristics are investigated by means of harmonic analysis method, matrix theory and operator theory, and three orthogonality formulas concerning the Wavelet Packets are presented. Orthogonal decomposition relation formulas of the space L 2 ( R n ) p are derived by designing a series of subspaces of the vector-valued Wavelet Packets. Moreover, several orthonormal Wavelet packet bases of L 2 ( R n ) p are constructed from the Wavelet Packets. Relation to some physical theories such as E-infinity theory and multifractal theory is also discussed.
-
The Presentation of a Class of Orthogonal Vector-Valued Multivariate Wavelet Packets Associated with an Integer-Valued Dilation Matrix
2009 International Conference on Environmental Science and Information Application Technology, 2009Co-Authors: Qingjiang Chen, Yongfeng PangAbstract:The notion of vector-valued multiresolution analysis of space of vector-valued higher-dimensional functions is introduced. An approach for constructing orthogonal vector-valued higher-dimensional Wavelet Packets is presented and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these Wavelet Packets are obtained. Finally, one new orthonormal bases of L2(Rp,Cr) are obtained by constructing a series of subspaces of orthogonal matrix-valued Wavelet Packets.
-
construction and characterizations of orthogonal vector valued multivariate Wavelet Packets
Chaos Solitons & Fractals, 2009Co-Authors: Qingjiang ChenAbstract:Abstract In this paper, the notion of orthogonal vector-valued Wavelet Packets of the space L 2 ( R s , C d ) is introduced. A method for constructing the orthogonal vector-valued Wavelet Packets is presented. Their properties are investigated by virtue of time–frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas with respect to the Wavelet Packets are established. Orthogonal decomposition relation formulas of L 2 ( R s , C d ) are obtained by constructing a series of subspaces of vector-valued Wavelet Packets. In particular, it is shown how to construct various orthonormal bases of L 2 ( R s , C d ) from these Wavelet Packets.
-
characterizations of a class of orthogonal multiple vector valued Wavelet Packets
International Journal of Wavelets Multiresolution and Information Processing, 2008Co-Authors: Qingjiang ChenAbstract:The notion of multiple vector-valued Wavelet Packets is introduced. A procedure for constructing the multiple vector-valued Wavelet Packets is presented. Their characteristics are investigated by means of integral transformation and operator theory, and three orthogonality formulas concerning the multiple vector-valued Wavelet Packets. Finally, new orthogonal bases of L2(R, Cs × s) are constructed from these multiple vector-valued Wavelet Packets.
-
construction and properties of orthogonal matrix valued Wavelets and Wavelet Packets
Chaos Solitons & Fractals, 2008Co-Authors: Qingjiang ChenAbstract:Abstract In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued Wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued Wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale orthogonal matrix-valued Wavelets is presented. The notion of orthogonal matrix-valued Wavelet Packets is proposed. Their properties are investigated by means of time–frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L2(R, Cr×r) from these Wavelet Packets, and the orthogonal decomposition relation is also given.
Amir Averbuch - One of the best experts on this subject based on the ideXlab platform.
-
image inpainting using directional Wavelet Packets originating from polynomial splines
Signal Processing-image Communication, 2021Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka Neittaanmaki, Moshe Salhov, Jonathan HauserAbstract:Abstract The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued Wavelet Packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.
-
image inpainting using directional Wavelet Packets originating from polynomial splines
arXiv: Image and Video Processing, 2020Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka Neittaanmaki, Moshe Salhov, Jonathan HauserAbstract:The paper presents a new algorithm for the image inpainting problem. The algorithm is using a recently designed versatile library of quasi-analytic complex-valued Wavelet Packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of the presented qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which, in essence, is the Split Bregman Iteration (SBI) procedure supplied with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.
-
periodic orthogonal Wavelets and Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal Wavelets and Wavelet Packets from discrete and discrete-time splines outlined in Chap. 3. These Wavelets and Wavelet Packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The Wavelet and Wavelet packet transforms are implemented in a fast way using the FFT.
-
detection of incipient bearing fault in a slowly rotating machine using spline Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:This chapter describes a successful application of spline-based Wavelet packet transforms (WPTs) described in Chap. 4 to a complicated problem of detection of incipient defects in rolling element bearings by the analysis of recorded vibration signals. The methodology presented in this chapter is applied to the analysis of vibration data recorded from large bearings working in real unfavorable operation conditions in presence of strong noise and vibrations from multiple internal and external sources. It relies on properties of discrete spline-based Wavelet Packets such as orthogonality, near-rectangular spectra, transient oscillating shapes of testing waveforms and fast implementation of transforms. The methodology succeeded in detection of even small defects that commercial vibration monitoring systems failed to detect. This chapter is written in cooperation with Kari Saarinen (Ph. D, ABB AB Corporate Research and Department of Mathematical Information Technology, University of Jyvaskyla, Finland).
-
two dimensional orthogonal Wavelets and Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:This chapter extends the design of spline-based orthogonal discrete-time Wavelets and Wavelet Packets to two-dimensional case. The corresponding transforms are implemented by using the 2D FFT.
Valery A. Zheludev - One of the best experts on this subject based on the ideXlab platform.
-
image inpainting using directional Wavelet Packets originating from polynomial splines
Signal Processing-image Communication, 2021Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka Neittaanmaki, Moshe Salhov, Jonathan HauserAbstract:Abstract The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued Wavelet Packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.
-
image inpainting using directional Wavelet Packets originating from polynomial splines
arXiv: Image and Video Processing, 2020Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka Neittaanmaki, Moshe Salhov, Jonathan HauserAbstract:The paper presents a new algorithm for the image inpainting problem. The algorithm is using a recently designed versatile library of quasi-analytic complex-valued Wavelet Packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of the presented qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which, in essence, is the Split Bregman Iteration (SBI) procedure supplied with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.
-
periodic orthogonal Wavelets and Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal Wavelets and Wavelet Packets from discrete and discrete-time splines outlined in Chap. 3. These Wavelets and Wavelet Packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The Wavelet and Wavelet packet transforms are implemented in a fast way using the FFT.
-
detection of incipient bearing fault in a slowly rotating machine using spline Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:This chapter describes a successful application of spline-based Wavelet packet transforms (WPTs) described in Chap. 4 to a complicated problem of detection of incipient defects in rolling element bearings by the analysis of recorded vibration signals. The methodology presented in this chapter is applied to the analysis of vibration data recorded from large bearings working in real unfavorable operation conditions in presence of strong noise and vibrations from multiple internal and external sources. It relies on properties of discrete spline-based Wavelet Packets such as orthogonality, near-rectangular spectra, transient oscillating shapes of testing waveforms and fast implementation of transforms. The methodology succeeded in detection of even small defects that commercial vibration monitoring systems failed to detect. This chapter is written in cooperation with Kari Saarinen (Ph. D, ABB AB Corporate Research and Department of Mathematical Information Technology, University of Jyvaskyla, Finland).
-
two dimensional orthogonal Wavelets and Wavelet Packets
2019Co-Authors: Amir Averbuch, Valery A. Zheludev, Pekka NeittaanmakiAbstract:This chapter extends the design of spline-based orthogonal discrete-time Wavelets and Wavelet Packets to two-dimensional case. The corresponding transforms are implemented by using the 2D FFT.
Qionghai Dai - One of the best experts on this subject based on the ideXlab platform.
-
fast adaptive Wavelet Packets using interscale embedding of decomposition structures
Pattern Recognition Letters, 2010Co-Authors: Jingyu Yang, Qionghai DaiAbstract:The most widely used basis selection algorithm for adaptive Wavelet Packets is the optimal basis selection method, which first grows a full Wavelet packet tree and then prunes it into the optimal tree that gives the minimum cost. We observed that there exists the interscale embedding property in Wavelet packet decomposition structures between interscale subbands along the same orientation. Based on this observation, we propose a fast basis selection algorithm by first decomposing a dyadic Wavelet subband with the decomposition structure of its parent subband, before applying the optimal basis selection method for further decomposition. Experiments show that the proposed algorithm generates almost the same Wavelet packet decomposition structures as the optimal basis selection method while significantly reducing the computational complexity for some image classes.
-
image and video denoising using adaptive dual tree discrete Wavelet Packets
IEEE Transactions on Circuits and Systems for Video Technology, 2009Co-Authors: Jingyu Yang, Yao Wang, Qionghai DaiAbstract:We investigate image and video denoising using adaptive dual-tree discrete Wavelet Packets (ADDWP), which is extended from the dual-tree discrete Wavelet transform (DDWT). With ADDWP, DDWT subbands are further decomposed into Wavelet Packets with anisotropic decomposition, so that the resulting Wavelets have elongated support regions and more orientations than DDWT Wavelets. To determine the decomposition structure, we develop a greedy basis selection algorithm for ADDWP, which has significantly lower computational complexity than a previously developed optimal basis selection algorithm, with only slight performance loss. For denoising the ADDWP coefficients, a statistical model is used to exploit the dependency between the real and imaginary parts of the coefficients. The proposed denoising scheme gives better performance than several state-of-the-art DDWT-based schemes for images with rich directional features. Moreover, our scheme shows promising results without using motion estimation in video denoising. The visual quality of images and videos denoised by the proposed scheme is also superior.
Jingyu Yang - One of the best experts on this subject based on the ideXlab platform.
-
fast adaptive Wavelet Packets using interscale embedding of decomposition structures
Pattern Recognition Letters, 2010Co-Authors: Jingyu Yang, Qionghai DaiAbstract:The most widely used basis selection algorithm for adaptive Wavelet Packets is the optimal basis selection method, which first grows a full Wavelet packet tree and then prunes it into the optimal tree that gives the minimum cost. We observed that there exists the interscale embedding property in Wavelet packet decomposition structures between interscale subbands along the same orientation. Based on this observation, we propose a fast basis selection algorithm by first decomposing a dyadic Wavelet subband with the decomposition structure of its parent subband, before applying the optimal basis selection method for further decomposition. Experiments show that the proposed algorithm generates almost the same Wavelet packet decomposition structures as the optimal basis selection method while significantly reducing the computational complexity for some image classes.
-
image and video denoising using adaptive dual tree discrete Wavelet Packets
IEEE Transactions on Circuits and Systems for Video Technology, 2009Co-Authors: Jingyu Yang, Yao Wang, Qionghai DaiAbstract:We investigate image and video denoising using adaptive dual-tree discrete Wavelet Packets (ADDWP), which is extended from the dual-tree discrete Wavelet transform (DDWT). With ADDWP, DDWT subbands are further decomposed into Wavelet Packets with anisotropic decomposition, so that the resulting Wavelets have elongated support regions and more orientations than DDWT Wavelets. To determine the decomposition structure, we develop a greedy basis selection algorithm for ADDWP, which has significantly lower computational complexity than a previously developed optimal basis selection algorithm, with only slight performance loss. For denoising the ADDWP coefficients, a statistical model is used to exploit the dependency between the real and imaginary parts of the coefficients. The proposed denoising scheme gives better performance than several state-of-the-art DDWT-based schemes for images with rich directional features. Moreover, our scheme shows promising results without using motion estimation in video denoising. The visual quality of images and videos denoised by the proposed scheme is also superior.
-
2-D anisotropic dual-tree complex Wavelet Packets and its application to image denoising
2008 15th IEEE International Conference on Image Processing, 2008Co-Authors: Jingyu Yang, Wenli Xu, Yao WangAbstract:In this paper, we extend the 2D dual-tree complex Wavelet transform (DTCWT) to an adaptive anisotropic dual- tree complex Wavelet Packets (ADTCWP). The DTCWT subbands are iteratively decomposed into anisotropic complex Wavelet Packets, generating anisotropic Wavelets and increasing the number of Wavelets orientations without introducing extra redundancy. Then a basis selection procedure is applied so that the selected complex Wavelet Packets are well adapted to image characteristics. The effectiveness of ADTCWP is examined in image denoising with a bivariate statistical model. The ADTCWP-based denoising scheme shows better denoising results than several DTCWT-based methods for image with rich directional features. The de-noised images recovered by the proposed scheme are visually more appealing.
