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Moreover, the computational complexity of the new method is equal to that of a discrete method, while squaring the sampling resolution in phase space. Cohen's class and trace class operators" Luef, Franz We study generalized localization operators from the perspective of quantum harmonic analysis which allows us to extend known results from the rank-one case to trace class operators.
The idea of localizing a signal to a domain in phase space is approached from various directions such as bounds on the spreading function, probability densities associated to generalized localization operators, positive operator valued measures, positive correspondence rules and variants of Tauberian theorems for operator translates. Our results include a rigorous treatment of multiwindow-STFT filters and a characterization of generalized localization operators as positive correspondence rules. Furthermore we provide a description of the Cohen class in terms of Werner's convolution of operators and deduce consequences on positive Cohen class distributions, an uncertainty principle, uniqueness and phase retrieval for general elements of Cohen's class.
View or edit your browsing history. Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation. Constructions of compactly supported, smooth orthogonal MRA wavelets in higher dimensions with isotropic dilations , on the other hand have proven to be elusive. Amazon Restaurants Food delivery from local restaurants. These spaces are completely different.
This is joint work with Eirik Skrettingland. Specifically, we prove that the stretched convex domain which captures the most positive lattice points in the large volume limit is balanced: A typical application is to higher-order Sobolev or trace embeddings.
A connection to the isoperimetric problem will be pointed out. Firstly, estimates are given for the remainder of Maclaurin series of those functions and consequent derivative sampling results are derived and discussed. These results are employed in evaluating the related remainder term of signals which occur in sampling series expansion of stochastic processes and random fields not necessarily stationary or homogeneous which spectral kernel satisfy the relaxed exponential boundedness.
The derived truncation error upper bounds enable to obtain mean-square master generalized derivative sampling series expansion formulae either for harmonizable Piranashvili-type stochastic processes or for random fields.
Finally, being the sampling series convergence rate exponential, almost sure P sampling series convergence rate is established. We then provide conditions that guarantee one iteration of an alternating dictionary learning scheme to contract an estimate for the desired generating dictionary towards this generating dictionary.
Conversely we will provide examples of dictionaries not equal to the generating dictionary that are stable fixed points of the alternating scheme. Based on these characterisations we then propose a cheap replacement strategy for alternate dictionary learning to escape local minima fixed points. Time permitting we will finally discuss how the replacement strategy can be used to automatically determine the dictionary size and sparsity level.
The main goal is to present several different interesting problems that may have not been studied as much as they deserve and where it seems possible to make progress. We analyze energy integrals with regard to area-regular partitions of the sphere and compare obtained estimates with discrete energy sums. Such type of operators, in particular Gabor frame multipliers, play an important role in signal processing.
It is of interest both for applications and from pure operator theory point of view, to determine cases where multipliers are invertible and corresponding formulas for the inversion. In this talk, first we present sufficient conditions for the invertibility of multipliers and formulas for the inverses via Neumann-type series.
Then we discuss representations of the inverses as multipliers based on appropriate dual frames of the initially given ones. In particular, we consider Gabor frame multipliers and cases where these appropriate dual frames also have a Gabor structure. The talk is based on a joint work with Peter Balazs. Derivatives of such functions are controlled by two-parameter dependent sequences which do not satisfy Komatsu's condition M. We present the result about superposition and inverse-closedness of such classes. This lead us to our main result: These results provide a systematic approach towards understanding the sparsity properties of different frame constructions including, but not limited to Gabor systems, wavelets, alpha-Gabor-wavelet frames, shearlets, and curvelets.
These spaces are a generalization of both Besov spaces and modulation spaces: Recall that Besov spaces can be defined using a dyadic partition of the Fourier domain, while modulation spaces use a uniform partition. General decomposition spaces are defined in the same way, but using an almost arbitrary covering of the frequency domain. If one chooses the frequency covering to be compatible with the frequency concentration of the frame, then the resulting decomposition space can be used to answer the preceding questions.
Even in these settings, our recent findings provide a unified perspective on various well-known results; moreover, they answer several open questions, in particular concerning the equivalence of questions 1 and 2 from above. Our main result can also be used to provide an alternative proof of recent lower bounds in the area of low-rank matrix recovery. In recent years fractional integral transforms, such as fractional Fourier, Laplace, Hankel, wavelets, and Radon transforms have been developed and they have shown promising results in many engineering and physical applications. However, convolution theorems for these transforms have not been fully developed.
The purpose of this talk is to introduce convolution theorems for some fractional transforms in one and several variables and derive analogues of Poisson summation formula. NO YES ordered by name "Wavelets functions WF and time dependant Density Functional Theory TDDFT application to quantum abinitio models for ultra-fast femtosecond photo emission" Babigeon, Jean-Luc Pseudo potential formalism - corresponding roughly to softening of short range potential near atomic sites - is compatible with many complete -or not- basis solutions of the Hamiltonian.
Particularly, WF basis are a demanding tool for the development of electronic wave function. They behave in a very efficient way regarding to plane wave development because of their localized character in real and reciprocal space, their orthogonality and smoothness, and finally, their adaptivity. It is a critical trend today, because even parallel simulations were recently limited to super lattices of some hundred of atoms.
Until now, implementation has been shown for ground states, GS, but few advances results have evaluated their possible use for excited states computations, inside the scope of TDDFT. However, that challenging task is not trivial: Finally we can't consider that in spatial grid, wave functions are null ''nearly everywhere''.
The present proposal is directed to 3 axes: Higher interactions like photo fields or optical field emission are not considered. Our goal in particle physics, is to develop a high repetition frequency femtosecond electron source, with very low charges per bunch. This context excludes simple electrical models ; thermodynamical and quantum effects on exotic armchair emitters like graphen may be preponderant.
By their plane geometry, our research presents also some analogies with the development of future nano scale electronic devices. For such a group G there is a Fourier-like transform F that identifies the algebra l1 G with a matrix algebra whose entries are functions in the Wiener algebra of the torus. The projections in l1 G are defined to be the self-adjoint idempotents. A well known collection of these are the sums of point masses over a finite subgroup of G. But are there other kinds of projections? For the 2-dimensional crystal group p2, we characterize projections in F l1 p2 and use this to construct projections in l1 p2 with interesting properties and which do not come from a finite subgroup.
In this situation Hilbert modules are not the right choice as they do not reflect the induced geometry and so-called Clifford-Krein modules appear as a natural answer. Even more, one needs the equivalent of Hilbert spaces with reproducing kernels. Here we are going discuss the theory of Clifford-Krein modules with reproducing kernels and present examples of its use like in the crystallographic X-ray transform and for ultrahyperbolic Dirac operators.
This is a Joint work with U. We study these operators from a time-frequency perspective, using the relative time-frequency representations. We provide sufficient conditions for the boundedness of these operators acting on modulation spaces and having symbols in weighted Wiener amalgam spaces. In this context, we find an upper bound for the operator norm which does not depend on the parameter, as expected. It is concerned with estimating the support of a sum of Dirac measures from a finite number of its Fourier coefficients. Similar to compressed sensing, the hope is to efficiently use the a priori information of sparsity, although sparsity in an infinite dimensional space is more difficult to exploit than in the finite dimensional case.
In this talk, we introduce a stability result for frequency estimation similar to the restricted isometric property.
Like in compressed sensing, we obtain a conditional well-posedness and a posteriori error estimates. To this end, we rely on extremal Fourier functions, which in turn can be motivated by classical results from sampling theory. The composition of the Blaschke functions induces a group in the set of the parameters, the so called Blaschke group. In order to construct analytic wavelets Pap and Schipp considered the voice transforms of this group and starting from published several results connected to this.
Instead of the Blascke group , we consider the analogue of it on the interval , the so called real Blaschke group. We introduce a representation of this group. We prove that this representation is unitary, and we consider the voice transform of the real Blaschke group induced by this representation. We use this representation to construct new orthogonal function systems.
We construct the characters of the subgroup. Consequently, we deduce similar results for several function systems including the case of TI systems, and GTI systems on compact abelian groups. We apply our results to the Bessel families having wave-packet structure combination of wavelet as well as Gabor structure , and hence a characterization for pairwise orthogonal wave-packet frame systems over LCA groups is obtained.
This is a joint work with Niraj Kumar Shukla, India. In search towards such a robust voice pathology detection system, we investigated three distinct classifiers within supervised learning and anomaly detection paradigms. We conducted a set of experiments using a variety of input data such as raw waveforms, spectrograms, mel-frequency cepstral coefficients MFCC , and conventional acoustic dysphonic features AF. Furthermore, to our best knowledge, this article is the first to explore gradient-boosted trees and deep learning for this application. The following best classification performances measured by F1 score on dedicated test set were achieved: Even though these results are of exploratory character, conducted experiments do show promising potential of gradient boosting and deep learning methods to robustly detect voice pathologies.
The resulting collection of functions is used to construct a time-frequency representation naturally adapted to the frequency progression defined by the given diffeomorphism.
This is joint work with Felix Voigtlaender "Weighted iterated Lp-Lq inequalities involving fractional convolution" Jain, Sandhya In this talk, we shall focus on three types of fractional convolutions. The famous Young's inequality in the context of fractional convolution will be discussed. We give generalized convolutions corresponding to these fractional convolutions.
The generalized Fourier convolution given by Nhan, Duc and Tuan comes as a special case of these generalized fractional convolutions. The weighted iterated norm inequalities in the framework of Lebesgue spaces will also be discussed. The duality principle between the frame and Riesz sequence properties of Gabor systems is a key result in time-frequency analysis. We present here the generalization of this theory to a duality between multi-window and super Gabor systems. The theory is established in the general setting of locally compact abelian groups. In this paper representations of the solution of a scattering problem in 2D using Gabor frames based on B-splines as building blocks are investigated and some properties of these frames will be shown based on numerical experiments.
An inversion formula for linear canonical wavelet packet transformation is also obtained.
Some examples are also discussed. In this paper, we provide an algorithm for the local reconstruction method and illustrate with an example along with implementation using Matlab. This joint work with Prof. We study the approximation of multivariate monotone functions based on information from function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number of function evaluations needed in order to approximate an unknown monotone function within a given error threshold grows at least exponentially in the dimension.
This is not the case in the randomized setting Monte Carlo setting where the complexity grows exponentially in the square-root of the dimension modulo logarithmic terms only. An algorithm exhibiting this complexity is presented. The algorithm is based on the Haar wavelet decomposition of monotone functions. Still, the problem remains difficult as best known methods are deterministic if the error threshold is comparably small. This inherent difficulty is confirmed by lower complexity bounds from which we deduce that the problem is not weakly tractable. Building upon the MIMO dual tiling condition, we derive reconstruction formulas for the channel operator's Kohn-Nirenberg symbol in closed form and discuss the problem of identifying MIMO channel operators where only restrictions in size, but not in location and geometry, of the subchannel spreading supports are known.
Joint work with Goetz Pfander and Volker Pohl. In our poster, we explore issues relating to coded excitation in high-frequency medical ultrasound, where the non-linear acoustic propagation in soft tissue and non-linear transducer characteristics reduce the SNR improvement and resolution achievable. Classical particle-mesh methods make use of the fast Fourier transform FFT to compute the interactions in pure charge systems subject to periodic boundary conditions in all three spatial directions. Particle systems containing a set of dipoles have already been studied as well and may be treated in a similar fashion.
Recently, this method has been generalized to 2d-periodic, 1d-periodic as well as open boundary conditions. In addition, the approach has been extended for the treatment of particle systems containing a mixture of charges and dipoles. The method is publicly available. Numerical results confirm that the method can be tuned to high accuracies. The HAP property is established for families of modulation spaces. Feichtinger in Wavelets-a tutorial in theory and applications, Academic Press, Boston, pp For the non-canonical dual frames obtained constructively in this way the HAP property is verified.
Several classes of permissible patterns are presented and it is shown how the corresponding window vector needs to be chosen. It is also shown that there exist support patterns for which no window generates a solvable linear system of equations. Estimates for translation and convolution function associated with the Kontorovich-Lebedev transform are obtained. Suboptimal greedy matching pursuit algorithms are generally used for such task. In this work, we present an acceleration technique of the matching pursuit algorithm acting on a multi-Gabor dictionary; a concatenation of several Gabor-type time-frequency dictionaries; each of which consisting of translations and modulations of a possibly different prototype window and time and frequency shift parameters.
The technique is based on pre-computing and thresholding inner products between atoms and on updating the residuum and the approximation error estimate directly in the coefficient domain i. In this manuscript, we review and study continuous frames in point of view of this operator. Despite being an efficient tool to analyze signals, it has not gained much popularity because of its non-bilinear nature i. The concept of controlled frames has been extended and generalized to g-frames in [3] and fusion frames in [4].
For the wavelet setting, inhomogeneous coorbit spaces have been obtained by Fornasier, Rauhut and Ullrich. Our construction is based on a generalization of this approach to the shearlet case. Furthermore, we present an atomic-like decomposition for these spaces which allows us to derive some properties. History, approach, and applications. Shape memory alloy actuators in smart structures: With Applications in Non-Homogeneous Media. Topics in Engineering, Volume Recent developments in geometrically nonlinear and postbuckling analysis of framed structures.
Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation. Applications to the Mexico City Valley. Applied Mathematical Sciences, Vol Topics in Engineering, Vol Moving Beyond the Finite Element Method.
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