ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 21 Jan 2020 17:12:45 GMT2020-01-21T17:12:45Z50301- Pairs of dual periodic frameshttps://scholarbank.nus.edu.sg/handle/10635/103911Title: Pairs of dual periodic frames
Authors: Christensen, O.; Goh, S.S.
Abstract: The time-frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients in the series expansions. The generality of the setup covers periodic frames of various types, including nonstationary wavelet systems, Gabor systems and certain hybrids of them. © 2012 Elsevier Inc. All rights reserved.
Thu, 01 Nov 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039112012-11-01T00:00:00Z
- Hybrid spline frameshttps://scholarbank.nus.edu.sg/handle/10635/103390Title: Hybrid spline frames
Authors: Goh, S.S.; Goodman, T.N.T.; Lee, S.L.
Abstract: Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for L2(R{double-struck}) consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for L2((0,∞)) comprising spline functions with knots on a hybrid of uniform and geometric mesh. The construction is motivated by applications in adaptive approximation using spline functions on a hybrid mesh that admits a natural dyadic multiresolution approximation of L2((0,∞)) based on dilation and translation. © 2009 American Mathematical Society.
Wed, 01 Jul 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033902009-07-01T00:00:00Z
- Pairs of oblique duals in spaces of periodic functionshttps://scholarbank.nus.edu.sg/handle/10635/103912Title: Pairs of oblique duals in spaces of periodic functions
Authors: Christensen, O.; Goh, S.S.
Abstract: We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials. © 2009 Springer Science+Business Media, LLC.
Thu, 01 Apr 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039122010-04-01T00:00:00Z
- Inequalities on time-concentrated or frequency-concentrated functionshttps://scholarbank.nus.edu.sg/handle/10635/103417Title: Inequalities on time-concentrated or frequency-concentrated functions
Authors: Goh, S.S.; Goodman, T.N.T.
Abstract: We obtain an inequality on a measure of the spread in time of periodic functions that are ε-concentrated in frequency, i.e. all but a fixed finite number of Fourier coefficients vanish with mean-squared error up to ε. We characterize an extremal function and give an asymptotic formula for the measure of spread of this extremal function as ε approaches 0. We also consider the corresponding problem for functions on the real line that are ε-concentrated in time or frequency. When ε=0, the above reduce to inequalities on time-limited or band-limited functions and these are discussed in more detail. © Springer 2006.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034172006-01-01T00:00:00Z
- Estimating maxima of generalized cross ambiguity functions, and uncertainty principleshttps://scholarbank.nus.edu.sg/handle/10635/103213Title: Estimating maxima of generalized cross ambiguity functions, and uncertainty principles
Authors: Goh, S.S.; Goodman, T.N.T.
Abstract: In certain signal processing problems, it is customary to estimate parameters in distorted signals by approximating what is termed a cross ambiguity function and estimating where it attains its maximum modulus. To unify and generalize these procedures, we consider a generalized form of the cross ambiguity function and give error bounds for estimating the parameters, showing that these bounds are lower if we maximize the real part rather than the modulus. We also reveal a connection between these bounds and certain uncertainty principles, which leads to a new type of uncertainty principle. © 2012 Elsevier Inc.
Fri, 01 Mar 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1032132013-03-01T00:00:00Z
- Band-limited refinable functions for wavelets and frameletshttps://scholarbank.nus.edu.sg/handle/10635/104673Title: Band-limited refinable functions for wavelets and framelets
Authors: Chen, W.; Goh, S.S.
Abstract: Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and biframes with desirable time-frequency localization. © 2010 Elsevier Inc. All rights reserved.
Sat, 01 May 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046732010-05-01T00:00:00Z
- Symmetric and antisymmetric tight wavelet frameshttps://scholarbank.nus.edu.sg/handle/10635/104686Title: Symmetric and antisymmetric tight wavelet frames
Authors: Goh, S.S.; Lim, Z.Y.; Shen, Z.
Abstract: For a given set of wavelets Ψ, we provide a general, and yet simple, method to derive a new set of wavelets Ψ′ such that each wavelet in Ψ′ is either symmetric or antisymmetric. The affine system generated by Ψ′ is a tight frame for the space L2 ( Rd ) whenever the affine system generated by Ψ is so. Further, when Ψ is constructed via a multiresolution analysis, Ψ′ can also be derived from a, but possibly different, multiresolution analysis. If moreover the multiresolution analysis for constructing Ψ is generated by a symmetric refinable function, then Ψ′ is obtained from the same multiresolution analysis. © 2005 Elsevier Inc. All rights reserved.
Mon, 01 May 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046862006-05-01T00:00:00Z
- Extension principles for tight wavelet frames of periodic functionshttps://scholarbank.nus.edu.sg/handle/10635/103257Title: Extension principles for tight wavelet frames of periodic functions
Authors: Goh, S.S.; Teo, K.M.
Abstract: A unitary extension principle for constructing normalized tight wavelet frames of periodic functions of one or higher dimensions is established. While the wavelets are nonstationary, the method much simplifies their construction by reducing it to a matrix extension problem that involves finite rows of complex numbers. Further flexibility is achieved by reformulating the result as an oblique extension principle. In addition, with a constructive proof, necessary and sufficient conditions for a solution of the matrix extension problem are obtained. A complete characterization of all possible solutions is also provided. As illustration, parametric families of trigonometric polynomial tight wavelet frames are constructed. © 2007 Elsevier Inc. All rights reserved.
Mon, 01 Sep 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1032572008-09-01T00:00:00Z
- An algorithm for constructing multidimensional biorthogonal periodic multiwaveletshttps://scholarbank.nus.edu.sg/handle/10635/104532Title: An algorithm for constructing multidimensional biorthogonal periodic multiwavelets
Authors: Goh, S.S.; Teo, K.M.
Abstract: This paper deals with the problem of constructing multidimensional biorthogonal periodic multiwavelets from a given pair of biorthogonal periodic multiresolutions. Biorthogonal polyphase splines are introduced to reduce the problem to a matrix extension problem, and an algorithm for solving the matrix extension problem is derived. Sufficient conditions for collections of periodic multiwavelets to form a pair of biorthogonal Riesz bases of the entire function space are also obtained.
Sun, 01 Oct 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1045322000-10-01T00:00:00Z
- Tight periodic wavelet frames and approximation ordershttps://scholarbank.nus.edu.sg/handle/10635/104379Title: Tight periodic wavelet frames and approximation orders
Authors: Goh, S.S.; Han, B.; Shen, Z.
Abstract: A systematic study on tight periodic wavelet frames and their approximation orders is conducted. We identify a necessary and sufficient condition, in terms of refinement masks, for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approximation orders of truncated tight frame series is established, which facilitates the construction of tight periodic wavelet frames with desirable approximation orders. Finally, a notion of vanishing moments for periodic wavelets, which is missing in the current literature, is introduced and related to frame approximation orders and sparse representations of locally smooth functions. As illustrations, the results are applied to two classes of examples: one is band-limited and the other is time-localized. © 2010 Elsevier Inc.
Thu, 01 Sep 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043792011-09-01T00:00:00Z
- Singular integrals, scale-space and wavelet transformshttps://scholarbank.nus.edu.sg/handle/10635/104124Title: Singular integrals, scale-space and wavelet transforms
Authors: Goh, S.S.; Goodman, T.N.T.; Lee, S.L.
Abstract: The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in Lp spaces. In the case of the Gaussian scale-space, the semi-discrete inversion formula can further be expressed as a sum of wavelet transforms with the even order derivatives of the Gaussian as mother wavelets. Similar results are obtained for B-spline scale-space, in which the high frequency component of a function between two consecutive dyadic scales can be represented as a finite linear combination of wavelet transforms with the derivatives of the B-spline or the spline framelets of Ron and Shen as mother wavelets. © 2013 Elsevier Inc.
Sun, 01 Dec 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1041242013-12-01T00:00:00Z
- From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versahttps://scholarbank.nus.edu.sg/handle/10635/103302Title: From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa
Authors: Christensen, O.; Goh, S.S.
Abstract: We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying the construction to Gabor frames generated by certain exponential B-splines yields wavelet frames generated by functions whose Fourier transforms are compactly supported splines with geometrically distributed knot sequences. On the other hand, the pendant of the Meyer wavelet turns out to be a tight Gabor frame generated by a C (R)function with compact support. Asanapplication of ourresults weshow that foreachgiven pairofbandlimiteddualwaveletframesitispossibletoconstructdualwaveletframesforad esiredscalingandtranslationparameters. © 2013 Elsevier Inc. All rights reserved.
Sat, 01 Mar 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033022014-03-01T00:00:00Z
- Uncertainty principles in Banach spaces and signal recoveryhttps://scholarbank.nus.edu.sg/handle/10635/104417Title: Uncertainty principles in Banach spaces and signal recovery
Authors: Song Goh, S.; Goodman, T.N.T.
Abstract: A very general uncertainty principle is given for operators on Banach spaces. Many consequences are derived, including uncertainty principles for Bessel sequences in Hilbert spaces and for integral operators between measure spaces. In particular it implies an uncertainty principle for Lp (G), 1 ≤ p ≤ ∞, for a locally compact Abelian group G, concerning simultaneous approximation of f ∈ Lp (G) by gf and H & f for suitable g and H. Taking g and over(H, ^) to be characteristic functions then gives an uncertainty principle about ε{lunate}-concentration of f and over(f, ^), which generalizes a result of Smith, which in turn generalizes a well-known result of Donoho and Stark. The paper also generalizes to the setting of Banach spaces a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise. In particular, this can be applied to the recovery of missing coefficients in a series expansion. © 2006 Elsevier Inc. All rights reserved.
Wed, 01 Nov 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044172006-11-01T00:00:00Z
- Fourier-like frames on locally compact abelian groupshttps://scholarbank.nus.edu.sg/handle/10635/128153Title: Fourier-like frames on locally compact abelian groups
Authors: Christensen, O.; Goh, S.S.
Thu, 01 Jan 2015 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1281532015-01-01T00:00:00Z
- Wavelet frames and shift-invariant subspaces of periodic functionshttps://scholarbank.nus.edu.sg/handle/10635/104461Title: Wavelet frames and shift-invariant subspaces of periodic functions
Authors: Goh, S.S.; Teo, K.M.
Abstract: A general approach based on polyphase splines, with analysis in the frequency domain, is developed for studying wavelet frames of periodic functions of one or higher dimensions. Characterizations of frames for shift-invariant subspaces of periodic functions and results on the structure of these subspaces are obtained. Starting from any multiresolution analysis, a constructive proof is provided for the existence of a normalized tight wavelet frame. The construction gives the minimum number of wavelets required. As an illustration of the approach developed, the one-dimensional dyadic case is further discussed in detail, concluding with a concrete example of trigonometric polynomial wavelet frames. © 2005 Elsevier Inc. All rights reserved.
Mon, 01 May 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044612006-05-01T00:00:00Z
- Joint estimation of time delay and Doppler shift for band-limited signalshttps://scholarbank.nus.edu.sg/handle/10635/115162Title: Joint estimation of time delay and Doppler shift for band-limited signals
Authors: Goh, S.S.; Goodman, T.N.T.; Shang, F.
Abstract: The standard approach for joint estimation of time delay and Doppler shift of a signal is to estimate the point at which the cross ambiguity function of the original and modified signals attains its maximum modulus. Since band-limited signals can be expressed exactly by their Shannon series, we here consider approximated signals gained by truncating their Shannon series to involve only the sampled signal values. We then estimate the time delay and Doppler shift by calculating a point at which the cross ambiguity function of the approximated signals attains its maximum modulus. This cross ambiguity function has an analytic expression which allows its evaluation at any point, and we may apply Newton's method to calculate accurately and efficiently a point where the maximum modulus is attained. In the numerical experiments we conducted, our method generally outperformed other methods for estimation of both time delay and Doppler shift. © 2006 IEEE.
Wed, 01 Sep 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151622010-09-01T00:00:00Z
- Uncertainty principles and asymptotic behaviorhttps://scholarbank.nus.edu.sg/handle/10635/104416Title: Uncertainty principles and asymptotic behavior
Authors: Goh, S.S.; Goodman, T.N.T.
Abstract: Various uncertainty principles for univariate functions are studied, including classes of such principles not considered before. For many uncertainty principles for periodic functions, the lower bound on the uncertainty is not attained. By considering Riemann sums, we show that for functions whose Fourier coefficients are sampled from the Gaussian with spacing h, the uncertainty approaches the lower bound as h → 0 with order O(h 2), whereas earlier work had shown at best O(h). We deduce that there is a sequence of trigonometric polynomials of degree k whose uncertainty approaches the lower bound with order O(1/k2) as k → ∞. We also establish a general uncertainty principle for n pairs of operators on a Hilbert space, n = 2,3,..., which allows us to extend the above univariate uncertainty principles to such principles for functions of n variables. Furthermore, we deduce an uncertainty principle for functions on the sphere double-struck S signn in ℝn+1, n = 2,3,..., generalizing known results for radial functions and for real-valued functions on double-struck S sign2. By considering the above work on univariate uncertainty principles, we can similarly derive, for all our multivariate uncertainty principles, sequences of functions for which the lower bound on the uncertainty is approached. © 2003 Elsevier Inc. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044162004-01-01T00:00:00Z
- Causality properties of refinable functions and sequenceshttps://scholarbank.nus.edu.sg/handle/10635/102969Title: Causality properties of refinable functions and sequences
Authors: Goh, S.S.; Goodman, T.N.T.; Lee, S.L.
Abstract: We show that the scale-space operators defined by a class of refinable kernels satisfy a version of the causality property, and a sequence of such operators converges to the corresponding operator with the Gaussian kernel, if the sequence of refinable kernels converges to the Gaussian function. In addition, we consider discrete analogs of these operators and show that a class of refinable sequences satisfies a discrete version of the causality property. The solutions of the corresponding discrete refinement equations are also investigated in detail. © 2006 Springer.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1029692007-01-01T00:00:00Z
- Constructing tight frames of multivariate functionshttps://scholarbank.nus.edu.sg/handle/10635/103047Title: Constructing tight frames of multivariate functions
Authors: Goh, S.S.; Goodman, T.N.T.; Lee, S.L.
Abstract: The paper presents a method of construction of tight frames for L2 (Ω), Ω ⊂ Rn. The construction is based on local orthogonal matrix extension of vectors associated with the transition matrices across consecutive resolution levels. Two explicit constructions are given, one for linear splines on triangular polygonal surfaces with arbitrary topology and the other for quadratic splines associated with Powell-Sabin elements on a six-direction mesh. © 2008 Elsevier Inc. All rights reserved.
Fri, 01 May 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030472009-05-01T00:00:00Z
- 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
- Uncertainty principles in Hilbert spaceshttps://scholarbank.nus.edu.sg/handle/10635/104418Title: Uncertainty principles in Hilbert spaces
Authors: Goh, S.S.; Micchelli, C.A.
Abstract: In this article we provide several generalizations of inequalities bounding the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty principle and time/frequency analysis of periodic functions. We develop conditions that ensure these inequalities are sharp and apply our results to concrete examples of importance in the literature.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044182002-01-01T00:00:00Z
- Uncertainty products of local periodic waveletshttps://scholarbank.nus.edu.sg/handle/10635/104419Title: Uncertainty products of local periodic wavelets
Authors: Goh, S.S.; Yeo, C.H.
Abstract: This paper is on the angle-frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated by periodic weighted convolutions, and it includes the well-known periodic B-splines and trigonometric B-splines. © J.C. Baltzer AG, Science Publishers.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1044192000-01-01T00:00:00Z
- Functionals of higher derivative typehttps://scholarbank.nus.edu.sg/handle/10635/103307Title: Functionals of higher derivative type
Authors: Goh, S.S.
Abstract: Functionals of higher derivative type are linear combinations of functionals of the form f→f(n)(ζ), where n ≥ 2 and 0 < |ζ| < 1. The paper shows that, if L is a functional of higher derivative type and f is a function in the class S of univalent functions that maximises Re{L} over S, then L(f) ≠ 0. In addition, if the function f is a rational function, then it must be a rotation of the Koebe function k(z) = z(1 - z)-2. These results are applied to establish several cases of the two-functional conjecture for functionals of higher derivative type.
Sat, 01 Aug 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033071998-08-01T00:00:00Z
- 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
- Construction of schauder decomposition on banach spaces of periodic functionshttps://scholarbank.nus.edu.sg/handle/10635/103054Title: Construction of schauder decomposition on banach spaces of periodic functions
Authors: Goh, S.S.; Lee, S.L.; Shen, Z.; Tang, W.S.
Abstract: This paper deals with Schauder decompositions of Banach spaces X2x of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,..., which form a multiresolution of X2x. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space L2x 2 on one hand and by interpolatory projections in the Banach space C2x on the other. The approach, using "orthogonal splines", is constructive and leads to the construction of a Schauder decomposition of X2x and a biorthogonal system for X2x and its dual X2x*. Decomposition and reconstruction algorithms are derived from the construction.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030541998-01-01T00:00:00Z
- Multidimensional periodic multiwaveletshttps://scholarbank.nus.edu.sg/handle/10635/103575Title: Multidimensional periodic multiwavelets
Authors: Goh, S.S.; Lee, S.L.; Teo, K.M.
Abstract: Necessary and sufficient conditions are given for the convergence of infinite products of matrices of complex numbers. The results are applied to the solution of periodic matrix refinement equations. Conditions are given for the solutions to be inL2([0, 2π)s) and generate a multiresolution of multiplicityr. A general algorithm for constructing multidimensional periodic multiwavelets from a scaling vector which generates a multiresolution is also given. © 1999 Academic Press.
Sat, 01 May 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035751999-05-01T00:00:00Z
- Matrix extension and biorthogonal multiwavelet constructionhttps://scholarbank.nus.edu.sg/handle/10635/103529Title: Matrix extension and biorthogonal multiwavelet construction
Authors: Goh, S.S.; Yap, V.B.
Abstract: Suppose that P(z) and P̃(z) are two r × n matrices over the Laurent polynomial ring ℛ[z], where r < n, which satisfy the identity P(z)P̃(z)* = Ir on the unit circle double-struct T sign. We develop an algorithm that produces two n × n matrices Q(z) and Q̃(z) over ℛ[z], satisfying the identity Q(z)Q̃(z)* = In on double-struct T sign, such that the submatrices formed by the first r rows of Q(z) and Q(z) are P(z) and P(z) respectively. Our algorithm is used to construct compactly supported biorthogonal multiwavelets from multiresolutions generated by univariate compactly supported biorthogonal scaling functions with an arbitrary dilation parameter m ∈ ℤ, where m > 1. © 1998 Elsevier Science Inc.
Thu, 15 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035291998-01-15T00:00:00Z
- 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
- Reconstruction of bandlimited signals from irregular sampleshttps://scholarbank.nus.edu.sg/handle/10635/104035Title: Reconstruction of bandlimited signals from irregular samples
Authors: Goha, S.S.; Ong, I.G.H.
Abstract: The classical theorem of Shannon enables one to reconstruct a finite-energy, bandlimited signal from a set of regularly spaced samples. Recently, Benedetto and Heller applied the theory of frames to derive a series of sampling theorems with irregularly spaced sampling sequences. In this paper, we study one of these theorems with emphasis on its implementation. To implement the theorem, sampling sequences and sampled coefficients are required. Here, general schemes to construct sampling sequences, and to evaluate sampled coefficients, are established. In addition, we provide an error analysis on the approximation of sampled coefficients. Numerical results are furnished to illustrate the theory and to study various related issues. These issues include the choice of sampling sequences and functions, the effect of truncating the sampling formula, and the influence of the irregularity of sampling sequences. © 1995.
Sun, 01 Oct 1995 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040351995-10-01T00:00:00Z
- Automated microaneurysm segmentation and detection using generalized eigenvectorshttps://scholarbank.nus.edu.sg/handle/10635/43221Title: Automated microaneurysm segmentation and detection using generalized eigenvectors
Authors: Pallawala, P.M.D.S.; Hsu, W.; Lee, M.L.; Goh, S.S.
Abstract: Diabetic retinopathy is a major cause of blindness and microaneurysms are the first clinically observable manifestations of diabetic retinopathy. Regular screening and timely intervention can halt or reverse the progression of this disease. This paper describes an approach that is based on the generalized eigenvectors of affinity matrix to extract microaneurysms from digital retinal images. Microaneurysms are in the low intensity regions and detection is complicated by their small sizes, the presence of retinal vessels, and their similarity to another type of retinal abnormality - haemorrhages. In order to accurately detect microaneurysms, the affinity matrix is defined to suppress larger structures such as blood vessels, haemorrhages, etc and to create uniform affinity distribution for pixels belonging to microaneurysms. The generalized eigenvector solution seeks to find the optimal segmentation for microaneurysms and provides indication to the possible locations of microaneurysms. We differentiate the true microaneurysms by studying their feature characteristics. Experiments on 70 retinal sub-images of diabetic, patients indicate that we are able to achieve 93% accuracy in the detection of microaneurysms.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/432212007-01-01T00:00:00Z