This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be...A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be simply presented. A brief overview of muhiwavelets is presented at first. Iris identification system and iris texture feature presentation and recognition based on multiwavelets a,e introduced subsequently. And the experiment indicates the validity of this method finally.展开更多
A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to...A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to classify the textures in the presence of additive white Gaussian noise (AWGN). The proposed approach extracts features such as energy, entropy, local homogeneity and max-min ratio from the selected singular values of multiwavelets transformation coefficients of image textures. The classification was carried out using probabilistic neural network (PNN). Performance of the proposed approach was compared with conventional wavelet domain gray level co-occurrence matrix (GLCM) based features, discrete multiwavelets transformation energy based approach, and HMM based approach. Experimental results showed the superiority of the proposed algorithms when compared with existing algorithms.展开更多
In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-leve...In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-level decomposition of the function and uses the method of the valve's value to construct adaptive grid to improve AUSMPW scheme.The obtained press and density have beed compared with those of results calculated by original AUSMPW scheme and WENO scheme.The numerical results demonstrate that this method has higher resolution.展开更多
A general method for constructing bidimensional orthogonal nonseparable mul- tiwavelets is presented. Moreover, this construction method can be extended to the con- struction of n-dimensional multiwavelets. In additio...A general method for constructing bidimensional orthogonal nonseparable mul- tiwavelets is presented. Moreover, this construction method can be extended to the con- struction of n-dimensional multiwavelets. In addition, we also study some properties of the multiwavelets such as balancing. Finally, we give an-example to illustrate our method to construct bidimensional nonseparable compactly supported orthogonal multiwavelets.展开更多
In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition ...In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.展开更多
In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelet...In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelets have several scaling functions and wavelet functions, and possess excellent properties that a scalar wavelet cannot satisfy simultaneously, and match the different characteristics of signals. Moreover, the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising. Therefore, the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process. The algorithm of bal- anced orthogonal multiwavelet and the implementation steps of this denoising are described. The experimental compar- ison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done. The experi- ments indieate that this method is effective and feasible to extract the fault feature submerged in heavy noise.展开更多
Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length bior...Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.展开更多
From the view of Optimum Time-Frequency Resolution (OPTFR), Jiang constructedorthogonal and symmetric multiwavelets Ψ_2, which has approximation order 2 and is supported in[0, 2]. In order to satisfy the highpass and...From the view of Optimum Time-Frequency Resolution (OPTFR), Jiang constructedorthogonal and symmetric multiwavelets Ψ_2, which has approximation order 2 and is supported in[0, 2]. In order to satisfy the highpass and lowpass property, we apply balancing technique tomatrix conjugate quadrature filters, then utilize the balanced matrix conjugate quadrature filtersfor fusion of images, and obtain expectant results.展开更多
In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x):= (φ1(x), ..., φr(x)) T is...In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x):= (φ1(x), ..., φr(x)) T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x):= (φ 1 new (x), ..., φ r new (x)) T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally, we reveal the relation between Φ(x) and Φnew(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4.展开更多
The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the ...The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the inshore area of China Sea,Single species cultures of 51 phytoplankton species were employed.The second scale vector (Ca2) of SA4,Ca2 of GHM and the third scale vector (Ca3) of coif2 were selected as feature spectra by Bayesian discriminate analysis (BDA).The reference spectra were obtained via hierarchical cluster analysis (HCA).With average high correct discrimination ratios (CDRs),reference spectra were representative to phytoplankton species.For one-algae samples,the average CDRs were 95.6% at genus level and 86.7% at division level.For the laboratory mixed samples,the average CDRs (one division accounted for 25%,75% or 100% of the total biomass) were 86.6%,91.4% and 100% at division level.Moreover,the average CDRs of the dominant species (accounted for 75%) was 79.8% at genus level.Results for the in situ samples were coincided with the microscopic ones at division level with the relative contents of 54.3%-96.5%.The fluorometric discriminating technique was further tested during the cruise in Bohai Sea recently.展开更多
A novel blind digital watermarking algorithm based on neural networks and multiwavelet transform is presented. The host image is decomposed through multiwavelet transform. There are four subblocks in the LL- level of ...A novel blind digital watermarking algorithm based on neural networks and multiwavelet transform is presented. The host image is decomposed through multiwavelet transform. There are four subblocks in the LL- level of the multiwavelet domain and these subblocks have many similarities. Watermark bits are added to low- frequency coefficients. Because of the learning and adaptive capabilities of neural networks, the trained neural networks almost exactly recover the watermark from the watermarked image. Experimental results demonstrate that the new algorithm is robust against a variety of attacks, especially, the watermark extraction does not require the original image.展开更多
Synthetic aperture radar （SAR） images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavel...Synthetic aperture radar （SAR） images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees （SPIHT） algorithm, our method achieves favorable peak signal to noise ratio （PSNR） and superior speckle noise reduction performances.展开更多
This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these ...This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.展开更多
In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solut...In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.展开更多
The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperfor...The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.展开更多
Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are n...Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.展开更多
Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our appro...Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our approach is that it uses a new Clifford-multiwavelet transform to insert copyright data in a multiresolution domain,allowing us to greatly expand the size of the watermark.After that,our method does two rounds of insertion,each applying a different type of Clifford-wavelet transform.Before being placed into the Clifford-multiwavelet coefficients,the watermark,which is a mixture of the mesh description,source mesh signature(produced using SHA512),and a logo encrypted using the RSA(Ronald Shamir Adleman)technique,is encoded using Turbo-code.Using the Least Significant Bit method steps,data embedding involves modulation and insertion processes.Finally,the watermarked mesh is reconstructed using the inverse Cliffordmultiwavelet transform.Due to the utilization of a hybrid insertion domain,our technique has demonstrated a very high insertion rate while retaining mesh quality.The mesh is watermarked,and the extracted data is acquired in real-time.Our approach is also resistant to the most common types of attacks.Our findings reveal that the current approach improves on previous efforts.展开更多
Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize....Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize. Compared with Wornell's single wavelet method, the new method has r filtering factors at each scale and has higher filtering speed, where r is the multiplicity of multiwavelet. Also due to the advantages of multiwavelet, the multiwavelet method performs better than that of Wornell's. Simulation results verify the analysis, and Wornell's method is the special case of our method when r = 1.展开更多
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
文摘A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be simply presented. A brief overview of muhiwavelets is presented at first. Iris identification system and iris texture feature presentation and recognition based on multiwavelets a,e introduced subsequently. And the experiment indicates the validity of this method finally.
文摘A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to classify the textures in the presence of additive white Gaussian noise (AWGN). The proposed approach extracts features such as energy, entropy, local homogeneity and max-min ratio from the selected singular values of multiwavelets transformation coefficients of image textures. The classification was carried out using probabilistic neural network (PNN). Performance of the proposed approach was compared with conventional wavelet domain gray level co-occurrence matrix (GLCM) based features, discrete multiwavelets transformation energy based approach, and HMM based approach. Experimental results showed the superiority of the proposed algorithms when compared with existing algorithms.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50476028)
文摘In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-level decomposition of the function and uses the method of the valve's value to construct adaptive grid to improve AUSMPW scheme.The obtained press and density have beed compared with those of results calculated by original AUSMPW scheme and WENO scheme.The numerical results demonstrate that this method has higher resolution.
文摘A general method for constructing bidimensional orthogonal nonseparable mul- tiwavelets is presented. Moreover, this construction method can be extended to the con- struction of n-dimensional multiwavelets. In addition, we also study some properties of the multiwavelets such as balancing. Finally, we give an-example to illustrate our method to construct bidimensional nonseparable compactly supported orthogonal multiwavelets.
文摘In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.
基金supported by Scientific and Technological Foundation of Henan Province under Grant No.112102210128Science Research Project of Educational Department of Henan Province under Grant No.2011C510005
文摘In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelets have several scaling functions and wavelet functions, and possess excellent properties that a scalar wavelet cannot satisfy simultaneously, and match the different characteristics of signals. Moreover, the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising. Therefore, the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process. The algorithm of bal- anced orthogonal multiwavelet and the implementation steps of this denoising are described. The experimental compar- ison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done. The experi- ments indieate that this method is effective and feasible to extract the fault feature submerged in heavy noise.
文摘Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.
基金This work is supported by the National Natural Science Foundation of China (No.10347138) and the National Natural Science Foundation of the Education Committeeof Shaanxi province(No.03JK062).
文摘From the view of Optimum Time-Frequency Resolution (OPTFR), Jiang constructedorthogonal and symmetric multiwavelets Ψ_2, which has approximation order 2 and is supported in[0, 2]. In order to satisfy the highpass and lowpass property, we apply balancing technique tomatrix conjugate quadrature filters, then utilize the balanced matrix conjugate quadrature filtersfor fusion of images, and obtain expectant results.
基金supported by the Natural Science Foundation of Guangdong Province (Grant Nos. 05008289,032038)the Doctoral Foundation of Guangdong Province (Grant No. 04300917)
文摘In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x):= (φ1(x), ..., φr(x)) T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x):= (φ 1 new (x), ..., φ r new (x)) T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally, we reveal the relation between Φ(x) and Φnew(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4.
基金supported by National High-Tech Research and Development Program of China (863 Program) (2009AA063005)Natural Science Foundation of Shandong Province (ZR2009EM001)Natural Science Foundation of China (40976060)
文摘The 3D fluorescence discrimination of phytoplankton classes was investigated by SA4 multiwavelet,GHM multiwavelet,and coifman-2(coif2) wavelet analysis.Belonging to 35 genera of 7 major phytoplankton divisions in the inshore area of China Sea,Single species cultures of 51 phytoplankton species were employed.The second scale vector (Ca2) of SA4,Ca2 of GHM and the third scale vector (Ca3) of coif2 were selected as feature spectra by Bayesian discriminate analysis (BDA).The reference spectra were obtained via hierarchical cluster analysis (HCA).With average high correct discrimination ratios (CDRs),reference spectra were representative to phytoplankton species.For one-algae samples,the average CDRs were 95.6% at genus level and 86.7% at division level.For the laboratory mixed samples,the average CDRs (one division accounted for 25%,75% or 100% of the total biomass) were 86.6%,91.4% and 100% at division level.Moreover,the average CDRs of the dominant species (accounted for 75%) was 79.8% at genus level.Results for the in situ samples were coincided with the microscopic ones at division level with the relative contents of 54.3%-96.5%.The fluorometric discriminating technique was further tested during the cruise in Bohai Sea recently.
基金The National Natural Science Foundation of China(No60473015)
文摘A novel blind digital watermarking algorithm based on neural networks and multiwavelet transform is presented. The host image is decomposed through multiwavelet transform. There are four subblocks in the LL- level of the multiwavelet domain and these subblocks have many similarities. Watermark bits are added to low- frequency coefficients. Because of the learning and adaptive capabilities of neural networks, the trained neural networks almost exactly recover the watermark from the watermarked image. Experimental results demonstrate that the new algorithm is robust against a variety of attacks, especially, the watermark extraction does not require the original image.
基金This work was supported by the National Natural Science Foundation of China under Grant No. 60472048.
文摘Synthetic aperture radar （SAR） images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees （SPIHT） algorithm, our method achieves favorable peak signal to noise ratio （PSNR） and superior speckle noise reduction performances.
文摘This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.
文摘In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.
文摘The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.
基金Project supported by the National Natural Science Foundation of China(Grant No.60672160)the Development Foundation of Shanghai Municipal Commission of Education(Grant No.05AZ42)
文摘Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.
基金This research work was funded by the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia through the project number(IF-PSAU-2021/01/17567)。
文摘Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our approach is that it uses a new Clifford-multiwavelet transform to insert copyright data in a multiresolution domain,allowing us to greatly expand the size of the watermark.After that,our method does two rounds of insertion,each applying a different type of Clifford-wavelet transform.Before being placed into the Clifford-multiwavelet coefficients,the watermark,which is a mixture of the mesh description,source mesh signature(produced using SHA512),and a logo encrypted using the RSA(Ronald Shamir Adleman)technique,is encoded using Turbo-code.Using the Least Significant Bit method steps,data embedding involves modulation and insertion processes.Finally,the watermarked mesh is reconstructed using the inverse Cliffordmultiwavelet transform.Due to the utilization of a hybrid insertion domain,our technique has demonstrated a very high insertion rate while retaining mesh quality.The mesh is watermarked,and the extracted data is acquired in real-time.Our approach is also resistant to the most common types of attacks.Our findings reveal that the current approach improves on previous efforts.
基金Supported by the National Laboratory of Space Microwave Technology Foundation(No.51473030105JB3201).
文摘Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize. Compared with Wornell's single wavelet method, the new method has r filtering factors at each scale and has higher filtering speed, where r is the multiplicity of multiwavelet. Also due to the advantages of multiwavelet, the multiwavelet method performs better than that of Wornell's. Simulation results verify the analysis, and Wornell's method is the special case of our method when r = 1.
