ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 17 Jan 2022 17:38:13 GMT2022-01-17T17:38:13Z50151- Convergence of cascade algorithms associated with nonhomogeneous refinement equationshttps://scholarbank.nus.edu.sg/handle/10635/103070Title: Convergence of cascade algorithms associated with nonhomogeneous refinement equations
Authors: Jia, R.-Q.; Jiang, Q.; Shen, Z.
Abstract: This paper is devoted to a study of multivariate nonhomogeneous refinement equations of the form φ(x) = g(x) + ∑αεℤs α(α)φ(Mx - α), x ε ℝs, where φ = (φ1,. . . , φr)T is the unknown, g = (g1,. . . , gr)T is a given vector of functions on ℝs, M is an s × s dilation matrix, and a is a finitely supported refinement mask such that each α(α) is an r × r (complex) matrix. Let φ0 be an initial vector in (L2(ℝs))r. The corresponding cascade algorithm is given by φk= φ + ∑αεℤs α(α)φk-1(M · - α), k = 1,2, . . . . In this paper we give a complete characterization for the L2-convergence of the cascade algorithm in terms of the refinement mask a, the nonhomogeneous term g, and the initial vector of functions φ0. © 2000 American Mathematical Society.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030702001-01-01T00:00:00Z
- Local discriminant time-frequency atoms for signal classificationhttps://scholarbank.nus.edu.sg/handle/10635/103510Title: Local discriminant time-frequency atoms for signal classification
Authors: Jiang, Q.; Goh, S.S.; Lin, Z.
Abstract: Three methods to select discriminant time-frequency atoms from the Gabor time-frequency dictionary are proposed. The first method performs a discriminant pursuit in its selection, the second method leads to atoms with the most discriminant power, and the third method combines the first two methods. The time-frequency atoms selected by the methods extract discriminant features among different classes of signals. Experimental results on the classification of simulated data sets (triangular waveforms) and real data sets (speech signals) using the extracted features are presented. © 1999 Elsevier Science B.V. All rights reserved.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035101999-01-01T00:00:00Z
- Distributional solutions of nonhomogeneous discrete and continuous refinement equationshttps://scholarbank.nus.edu.sg/handle/10635/103149Title: Distributional solutions of nonhomogeneous discrete and continuous refinement equations
Authors: Rong-Qing, J.; Jiang, Q.; Shen, Z.
Abstract: Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no "universal" theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneously. In this paper, we provide a uniform treatment for both equations. In particular, a complete characterization of the existence of distributional solutions of nonhomogeneous discrete and continuous refinement equations is given, which covers all cases of interest. © 2000 Society for Industrial and Applied Mathematics.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031492000-01-01T00:00:00Z
- Multivariate matrix refinable functions with arbitrary matrix dilationhttps://scholarbank.nus.edu.sg/handle/10635/103594Title: Multivariate matrix refinable functions with arbitrary matrix dilation
Authors: Jiang, Q.
Abstract: Characterizations of the stability and orthonormality of a multivariate matrix refinable function φ with arbitrary matrix dilation M are provided in terms of the eigenvalue and 1-eigenvector properties of the restricted transition operator. Under mild conditions, it is shown that the approximation order of φ is equivalent to the order of the vanishing moment conditions of the matrix refinement mask {Pα}. The restricted transition operator associated with the matrix refinement mask {Pα} is represented by a finite matrix (AMi-j)i,j, with Aj = |det(M)|-1 ∑κ Pκ-j ⊗ Pκ and Pκ-j ⊗ Pκ being the Kronecker product of matrices Pκ-j and Pκ. The spectral properties of the transition operator are studied. The Sobolev regularity estimate of a matrix refinable function φ is given in terms of the spectral radius of the restricted transition operator to an invariant subspace. This estimate is analyzed in an example. ©1999 American Mathematical Society.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035941999-01-01T00:00:00Z
- Wavelet transform and orthogonal decomposition of L2 space on the cartan domain BDI(q = 2)https://scholarbank.nus.edu.sg/handle/10635/104462Title: Wavelet transform and orthogonal decomposition of L2 space on the cartan domain BDI(q = 2)
Authors: Jiang, Q.
Abstract: Let G = (R+ × SO0(1,n)) × Rn+1 be the Weyl-Poincaré group and K AN be the Iwasawa decomposition of SOo(l, n) with K = SO(n). Then the "affine Weyl-Poincaré group" Ga = (R+. × AN) × Rn+1 can be realized as the complex tube domain II = Rn+1 + iC or the classical Cartan domain BDI(q = 2). The square-integrable representations of G and Ga give the admissible wavelets and wavelet transforms. An orthogonal basis of the set of admissible wavelets associated to Ga is constructed, and it gives an orthogonal decomposition of L2 space on II (or the Cartan domain BDI(q = 2)) with every component Ak. being the range of wavelet transforms of functions in H2 with k. ©1997 American Mathematical Society.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044621997-01-01T00:00:00Z
- Parameterization of m-channel orthogonal multifilter bankshttps://scholarbank.nus.edu.sg/handle/10635/103914Title: Parameterization of m-channel orthogonal multifilter banks
Authors: Jiang, Q.
Abstract: A complete parameterization for the m-channel FIR orthogonal multifilter banks is provided based on the lattice structure of the paraunitary systems. Two forms of complete factorization of the m-channel FIR orthogonal multifilter banks for symmetric/antisymmetric scaling functions and multiwavelets with the same symmetric center 1/2(1 + γ + γ/(m - 1)) for some nonnegative integer γ are obtained. For the case of multiplicity 2 and dilation factor m = 2, the result of the factorization shows that if the scaling function φ and multiwavelet ψ are symmetric/antisymmetric about the same symmetric center γ + 1/2 for some nonnegative integer γ, then one of the components of φ (respectively ψ) is symmetric and the other is antisymmetric. Two examples of the construction of symmetric/antisymmetric orthogonal multiwavelets of multiplicity 3 with dilation factor 2 and multiplicity 2 with dilation factor 3 are presented to demonstrate the use of these parameterizations of orthogonal multifilter banks. © J.C. Baltzer AG, Science Publishers.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039142000-01-01T00:00:00Z
- On the design of multifilter banks and orthogonal multiwavelet baseshttps://scholarbank.nus.edu.sg/handle/10635/103787Title: On the design of multifilter banks and orthogonal multiwavelet bases
Authors: Jiang, Q.
Abstract: Several forms of the parameter expressions for the orthogonal multifllter banks are presented. The explicit expressions for a group of the orthogonal multifllter banks that generate symmetric/antisymmetric scaling functions and orthogonal multiwavelets are obtained. The balanced multiwavelets that are multiwavelet pairs that are more suitable for image processing are discussed. Based on the parameter expressions for the orthogonal multifllter banks, the balanced multiwavelets that are multiwavelet pairs with better time-frequency localization properties are constructed, and the optimal multifllter banks are provided. ©1997 IEEE.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037871997-01-01T00:00:00Z
- On the regularity of matrix refinable functionshttps://scholarbank.nus.edu.sg/handle/10635/103832Title: On the regularity of matrix refinable functions
Authors: Jiang, Q.
Abstract: It is shown that the transition operator Tp associated with the matrix refinement mask P(ω) = 2-d∑α∈[0, N]dPαexp(-iαω) is equivalent to the matrix (2-dA2i-j)i,j with Aj = ∑κ∈[0, N]dPκ-j⊗Pκ and Pκ-j⊗Pκ denoting the Kronecker product of matrices Pκ-j, Pκ. Some spectral properties of Tp are studied and a complete characterization of the matrix refinable functions in the Sobolev space Wn(Rd) for nonnegative integers n is provided. The Sobolev regularity estimate of the matrix refinable function is given in terms of the spectral radius of a restricted transition operator. These estimates are analyzed in some examples.
Tue, 01 Sep 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1038321998-09-01T00:00:00Z
- On existence and weak stability of matrix refinable functionshttps://scholarbank.nus.edu.sg/handle/10635/103705Title: On existence and weak stability of matrix refinable functions
Authors: Jiang, Q.; Shen, Z.
Abstract: We consider the existence of distributional (or L2) solutions of the matrix refinement equation Φ̂ = P(·/2)Φ̂(·/2), where P is an r × r matrix with trigonometric polynomial entries. One of the main results of this paper is that the above matrix refinement equation has a compactly supported distributional solution if and only if the matrix P(0) has an eigenvalue of the form 2n, n ∈ ℤ+. A characterization of the existence of L2-solutions of the above matrix refinement equation in terms of the mask is also given. A concept of L2-weak stability of a (finite) sequence of function vectors is introduced. In the case when the function vectors are solutions of a matrix refinement equation, we characterize this weak stability in terms of the mask.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037051999-01-01T00:00:00Z
- Selection of initial parameters for signal representation by adaptive waveletshttps://scholarbank.nus.edu.sg/handle/10635/104085Title: Selection of initial parameters for signal representation by adaptive wavelets
Authors: Jiang, Q.; Goh, S.S.; Lim, N.C.; Lin, Z.
Abstract: Good initial parameters are important for the application of adaptive wavelets to signal representation. An algorithm for the selection of good initial parameters is presented. The algorithm introduces negligible additional computational complexity into the signal representation process. Its effectiveness is demonstrated by numerical results on the representation of signals obtained from contours of coastlines. © 1993 Society of Photo-Optical Instrumentation Engineers.
Tue, 01 Sep 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040851998-09-01T00:00:00Z
- Rotation invariant ambiguity functionshttps://scholarbank.nus.edu.sg/handle/10635/104070Title: Rotation invariant ambiguity functions
Authors: Jiang, Q.
Abstract: Let W(ψ; x, y) be the wideband ambiguity function. It is obtained in this note that y- α+2/2 W(ψ;x,y)(α > -1) is SO(2)-invariant if and only if the Fourier transform of ψ is a Laguerre function. ©1998 American Mathematical Society.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040701998-01-01T00:00:00Z
- Optimal multifilter banks: design, related symmetric extension transform, and application to image compressionhttps://scholarbank.nus.edu.sg/handle/10635/103872Title: Optimal multifilter banks: design, related symmetric extension transform, and application to image compression
Authors: Xia, T.; Jiang, Q.
Abstract: The design of optimal multifilter banks and optimum time-frequency resolution multiwavelets with different objective functions is discussed. The symmetric extension transform related to multifilter banks with the symmetric properties is presented. It is shown that such a symmetric extension transform is nonexpansive. More optimal multifilter banks for image compression are constructed, and some of them are used in image compression. Experiments show that optimal multifilter banks have better performances in image compression than Daubechies' orthogonal wavelet filters and Daubechies' least asymmetric wavelet filters, and for some images, they even have better performances than the scalar (9, 7)-tap biorthogonal wavelet filters. Experiments also show that the symmetric extension transform provided in this paper improves the rate-distortion performance compared with the periodic extension transform.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1038721999-01-01T00:00:00Z
- Toeplitz type operators on wavelet subspaceshttps://scholarbank.nus.edu.sg/handle/10635/104383Title: Toeplitz type operators on wavelet subspaces
Authors: Jiang, Q.; Peng, L.
Sat, 15 Mar 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043831997-03-15T00:00:00Z
- Construction of Biorthogonal Multiwavelets Using the Lifting Schemehttps://scholarbank.nus.edu.sg/handle/10635/115655Title: Construction of Biorthogonal Multiwavelets Using the Lifting Scheme
Authors: Goh, S.S.; Jiang, Q.; Xia, T.
Abstract: The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time-frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented. © 2000 Academic Press.
Wed, 04 Oct 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1156552000-10-04T00:00:00Z
- Orthogonal multiwavelets with optimum time-frequency resolutionhttps://scholarbank.nus.edu.sg/handle/10635/103884Title: Orthogonal multiwavelets with optimum time-frequency resolution
Authors: Jiang, Q.
Abstract: A procedure to design orthogonal multiwavelets with good time-frequency resolution is introduced. Formulas to compute the time-durations and the frequency-bandwidths of scaling functions and multiwavelets are obtained. Parameter expressions for the matrix coefficients of the multifllter banks that generate symmetric/antisymmetric scaling functions and multiwavelets supported in [0, N] are presented for N -2, 6. Orthogonal multiwavelets with optimum time-frequency resolution are constructed, and some optimal multifllter banks are provided.© 1998 IEEE.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1038841998-01-01T00:00:00Z