Showing papers on "Biorthogonal system published in 2017"
TL;DR: The designed three-band filter banks and multi-layer perceptron neural network (MLPNN) are further used together to implement a signal classifier that provides classification accuracy better than the recently reported results for epileptic seizure EEG signal classification.
114 citations
TL;DR: A new class of compactly supported antisymmetric biorthogonal wavelet filter banks which have the analysis as well as the synthesis filters of even-length are presented, designed to have minimum joint duration-bandwidth localization (JDBL).
47 citations
TL;DR: A simple and efficient parametrization technique is presented for constructing linear phase biorthogonal discrete-time wavelet bases that have joint timefrequency localization (JTFL) close to the lower bound of 0.25.
39 citations
TL;DR: In this article, the authors considered the problem of reducing the 12 coupled differential equations in the case M = 2 to a single differential equation for the resolvent, and showed that this simplifies to a simpler third-order nonlinear equation for general hard edge parameters.
Abstract: The squared singular values of the product of M complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a hard edge scaling to a form specified in terms of certain Meijer G-functions, or equivalently hypergeometric functions 0FM, also referred to as hyper-Bessel functions. In the case M=1, it is well known that the corresponding gap probability for no squared singular values in (0, s) can be evaluated in terms of a solution of a particular sigma form of the Painleve III' system. One approach to this result is a formalism due to Tracy and Widom, involving the reduction of a certain integrable system. Strahov has generalized this formalism to general M≥1, but has not exhibited its reduction. After detailing the necessary working in the case M=1, we consider the problem of reducing the 12 coupled differential equations in the case M=2 to a single differential equation for the resolvent. An explicit fourth-order nonlinear is found for general hard edge parameters. For a particular choice of parameters, evidence is given that this simplifies to a much simpler third-order nonlinear equation. The small and large s asymptotics of the fourth-order equation are discussed, as is a possible relationship of the M=2 systems to so-called four-dimensional Painleve-type equations.
33 citations
TL;DR: This paper proposes a general method for constructing wavelet bases on the interval [0,1] derived from symmetric biorthogonal multiwavelets on the real line that is based on the finite difference formula combined with the collocation method.
31 citations
TL;DR: In this article, the vanishing moment property of wavelets acting on vector data representing function values and consecutive derivatives has been investigated in the context of Hermite-type wavelet filters.
25 citations
TL;DR: A sampling theory for multidimensional non-decaying signals living in weighted Sobolev spaces was developed in this paper, where the sampling and reconstruction of an analog signal can be done by a projection onto a shift-invariant subspace generated by an interpolating kernel.
23 citations
TL;DR: In this article, the effects of dissipation on periodic lattice systems are effectively described by the potentials of the Berry phases of the system's non-Hermitian Hamiltonian, and a general numerical gauge smoothing procedure is developed to calculate complex Berry phases from the biorthogonal basis of the Hamiltonian.
Abstract: We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by $\mathcal{PT}$-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional $\mathcal{PT}$-symmetric lattice system and verify our numerical results by an analytical calculation.
22 citations
TL;DR: In this paper, the concept of quasi-basis was introduced for non-self-adjoint Hamiltonians with purely point real spectra, and a series of conditions under which such a definition is still possible.
Abstract: In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of -quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible.
22 citations
TL;DR: An extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space is discussed and some examples in detail are described.
Abstract: We review some basic definitions and a few facts recently established for D-pseudobosons and pseudofermions. We also discuss an extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space and describe some examples in detail.
13 citations
30 Dec 2017
TL;DR: In this article, the effects of dissipation are effectively described by PT-symmetric potentials, and a general numerical gauge smoothing procedure is developed to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian.
Abstract: We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by PT -symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional PT -symmetric lattice system and verify our numerical results by an analytical calculation.
TL;DR: In this paper, the authors review some basic definitions and few facts recently established for pseudo bosons and pseudo-fermions and discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space.
Abstract: We review some basic definitions and few facts recently established for $\D$-pseudo bosons and for pseudo-fermions. We also discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space. Some examples are described in details.
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TL;DR: In this article, the authors obtained Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces, and showed that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces.
Abstract: We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of non necessarily quasi-greedy bases.
TL;DR: In this paper, a generalized exact holographic mapping framework is proposed to preserve the form of a large class of lattice Hamiltonians by explicitly separating features that are fundamentally associated with the physical system from those that are basis specific.
Abstract: The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic $N$-dimensional lattice system to a ($N+1$)-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti--de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.
24 Sep 2017
TL;DR: A computationally light frequency domain feature extraction method based on lifting wavelet transform (LWT) which provides computational efficiency suitable for real-time low power devices such as wearable sensors for human fall detection.
Abstract: Frequency domain features of inertial movement enables multi-resolution analysis for fall detection, yet they are computationally intensive This paper proposes a computationally light frequency domain feature extraction method based on lifting wavelet transform (LWT) which provides computational efficiency suitable for real-time low power devices such as wearable sensors for human fall detection LWT is combined with support vector machine (SVM) to identify falls from activities of daily living Performance of the Haar and Biorthogonal 22 wavelets were compared with the time domain feature of root-mean square acceleration using a human fall dataset Results show that the first level detail coefficients features for both Haar and Biorthogonal 22 wavelets achieve good overall fall detection accuracy, sensitivity and specificity
TL;DR: In this paper, a large deviations principle for a class of biorthogonal ensembles with i.i.d. complex Gaussian entries was provided for the singular values of lower triangular random matrices with independent entries introduced by Cheliotis.
Abstract: This note provides a large deviations principle for a class of biorthogonal ensembles. We extend the results of Eichelsbacher, Sommerauer and Stotlz to more general type of interactions. Our result covers the case of the singular values of lower triangular random matrices with independent entries introduced by Cheliotis. In particular, we obtain as a consequence a variational formulation for the Dykema-Haagerup as it is the limit law for the singular values of lower triangular matrices with i.i.d. complex Gaussian entries.
TL;DR: In this article, the authors classify the closed simply-connected 4-manifolds that admit a Riemannian metric for which the average of pairs of sectional curvatures of orthogonal planes are positive.
Abstract: We classify, up to homeomorphisms, the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.
TL;DR: The Peak Signal-to-Noise Ratio (PSNR) and subjective effects of the reconstructed images using the proposed transform and image coding scheme are better at the same bit rates, especially at low bit rates.
Abstract: —To improve the coding performance in JPEG image compression and reduce the computational complexity, this paper proposes a new transform called All Phase Inverse Discrete Sine Biorthogonal Transform (APIDSBT) based on the All Phase Biorthogonal Transform (APBT) and Inverse Discrete Sine Transform (IDST). Similar to Discrete Sine Transform (DST) matrix and Discrete Cosine Transform (DCT) matrix, it can be used in image compression which transforms the image from spatial domain to frequency domain. Compared with other transforms in JPEG-like image compression algorithm, the Peak Signal-to-Noise Ratio (PSNR) and subjective effects of the reconstructed images using the proposed transform and image coding scheme are better at the same bit rates, especially at low bit rates. The advantage is that the quantization process is simpler and the computational complexity is lower.
TL;DR: This paper studies highly symmetric 3 -refinement wavelet bi-frames for surface processing and designs the frame algorithms based on the vanishing moments and smoothness of the framelets so that one can easily implement them.
TL;DR: In this article, a system of functionals biorthogonal to the system of minimal coordinate splines is constructed, and the results obtained are illustrated with an example of a polynomial generating vector function which leads to the construction of B-splines from the approximation relations.
Abstract: The paper considers minimal splines of Lagrange type of lower orders, and a system of functionals biorthogonal to the system of minimal coordinate splines is constructed. The results obtained are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines from the approximation relations. Bibliography: 16 titles.
01 Jan 2017
TL;DR: This work considers a simpler setting where M is a power of 2 and proposes a perfect reconstruction tree-structured biorthogonal filter bank solution comprised of a hierarchical 2-channel design.
Abstract: In this paper, we study the design of graph wavelet filter banks over M-block cyclic graphs. These graphs are natural directed extensions of bipartite graphs and their special structure is particularly suitable for the design of M-channel filter banks. Obtaining polynomial filter designs in this case that satisfy perfect reconstruction conditions is challenging since the Fourier domain of these graphs encompasses the entire complex-unit disc unlike just the complex unit-circle in the classical domain. Therefore, in this work, we consider a simpler setting where M is a power of 2 and propose a perfect reconstruction tree-structured biorthogonal filter bank solution comprised of a hierarchical 2-channel design. This approach significantly simplifies the design process by requiring the design of only one 2-channel filter bank for a directed bipartite graph, and repeating it across the hierarchy.
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TL;DR: In this paper, the authors extend some of the general results of Fattorini-Russell concerning biorthogonal families, using complex analysis techniques developed by Seidman, Guichal, Tenenbaum-Tucsnak and Lissy.
Abstract: A classical and useful way to study controllability problems is the moment method developed by Fattorini-Russell, based on the construction of suitable biorthogonal families. Several recent problems exhibit the same behaviour: the eigenvalues of the problem satisfy a uniform but rather 'bad' gap condition, and a rather 'good' but only asymptotic one. The goal of this work is to obtain general and precise upper and lower bounds for biorthogonal families under these two gap conditions, and so to measure the influence of the 'bad' gap condition and the good influence of the 'good' asymptotic one. To achieve our goals, we extend some of the general results of Fattorini-Russell concerning biorthogonal families, using complex analysis techniques developed by Seidman, Guichal, Tenenbaum-Tucsnak, and Lissy.
TL;DR: This paper reviews different types of wavelets that can be considered, the Cohen–Daubechies–Feauveau biorthogonal wavelets, the orthogonal Daubechie wavelets and the Deslauries–Dubuc interpolating wavelets.
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TL;DR: In this paper, the authors presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients and derived the ratio asymptotic for this family of matrices.
Abstract: In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived in quite general assumptions. It is considered some illustrative examples.
TL;DR: Inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, the stability of a sequence of spline-type spaces is approached as uniform boundedness of projection operators.
Abstract: In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis operator in Banach spaces of distributions. The constructive nature of the proof for Theorem 2 enabled us to constructively realize the biorthogonal system of a given one. Then, inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, we approached the stability of a sequence of spline-type spaces as uniform boundedness of projection operators. Through Theorem 3, we characterize stable sequences of stable spline-type spaces.
TL;DR: In this paper, the authors construct a system of entire functions of exponential type of class A biorthogonal with weight to some power system on the ray, where the indicator diagram of such a function is a segment of the imaginary axis.
Abstract: We construct a system of entire functions of exponential type of class A biorthogonal with weight to some power system on the ray. The indicator diagram of such a function is a segment of the imaginary axis. Functions analytic in a circular lacuna are represented by biorthogonal series.
23 Jun 2017
TL;DR: A replacement feature-based approach is proposed for automatic Deep-Sea image registration and stitching and is enforced on real complicated undersea pictures which rely on four main steps.
Abstract: The main construct behind Deep-Sea image stitching is a combined work of multiple underwater camera captured pictures with overlaying fields of view to produce a high-resolution and panoramic image registration. In image stitching many overlapping pictures are assembled so as to represent one bird's-eye image view. During this research, a replacement feature-based approach is proposed for automatic Deep-Sea image registration and stitching. The projected methodology is enforced on real complicated undersea pictures which rely on four main steps. First, the Harris Algorithm is employed to extract the feature points within the reference and detected pictures. Second, feature matching is applied for treating the geometer difference of the signature vectors are achieved by Biorthogonal multi wavelet Transformation. Third, transformation factors are achieved by treating the least-square rule supported by general wavelet transformation. Finally, the Picture resampling and transformation are executed for the treatment of additive interpolation which induces the image registration and image stitching.
TL;DR: In this article, the mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors are considered and their linear forms are investigated, which include explicit formulas, integral representations, differential properties, limiting forms and recurrence relations.
TL;DR: In this paper, a biorthogonality formalism for non-Hermitian multimode and multiphoton Jaynes-Cummings models is developed, where the Hamiltonian and its adjoint are expressed in terms of supersymmetric generators having the Lie superalgebra properties.
Abstract: We develop a biorthogonal formalism for non-Hermitian multimode and multiphoton Jaynes–Cummings models. For these models, we define supersymmetric generators, which are especially convenient for diagonalizing the Hamiltonians. The Hamiltonian and its adjoint are expressed in terms of supersymmetric generators having the Lie superalgebra properties. The method consists in using a similarity dressing operator that maps onto spaces suitable for diagonalizing Hamiltonians even in an infinite-dimensional Hilbert space. We then successfully solve the eigenproblems related to the Hamiltonian and its adjoint. For each model, the eigenvalues are real, while the eigenstates do not form a set of orthogonal vectors. We then introduce the biorthogonality formalism to construct a consistent theory.