Showing papers in "Applied and Computational Harmonic Analysis in 2019"

TL;DR: This work presents an efficient numerical algorithm that is guaranteed to recover the exact solution, when the number of measurements is slightly larger than the information-theoretical minimum, and under reasonable conditions on f and g.

TL;DR: In this paper, a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems is presented, based on a representation of the Koopman and Perron-Frobenius groups of unitary operators in a smooth orthonormal basis of the L 2 space of the dynamical system, acquired from time-ordered data through diffusion maps algorithm.

TL;DR: In this paper, the authors derived new CS results for structured acquisitions and signal satisfying a prior structured sparsity, and the obtained results are RIPless, in the sense that they do not hold for any s-sparse vector, but for sparse vectors with a given support S. Their results are thus support-dependent, and they offer the possibility for flexible assumptions on the structure of S.

TL;DR: In this article, the problem of reconstructing spectrally sparse signals from a random subset of n regular time domain samples is reformulated as a low rank Hankel matrix completion problem.

TL;DR: In this article, the authors introduce a graph structure for a distributed sampling and reconstruction system by coupling agents in a spatially distributed network with innovative positions of signals, and show that the stability of the sensing matrix holds if and only if its quasi-restrictions to those subsystems have uniform stability.

TL;DR: In this article, the authors show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements of the discrete Prolate Spheroidal Sequence (DPSS).

TL;DR: In this paper, the authors consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional.

TL;DR: This paper addresses the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations, and introduces a class of frames, called uniform covering frames, which includes a variety of semi-discrete Gabor systems.

TL;DR: In this paper, the quaternion embedding of bivariate signals is introduced, which is a bivariate counterpart of the usual analytic signal of real signals, and two fundamental theorems ensure that a quaternions short term Fourier transform (SFT) and quaternians continuous wavelet transform (CWT) obey desirable properties such as conservation laws and reconstruction formulas.

TL;DR: In this article, the authors consider the problem of non-negative super-resolution and show that non-negativity is sufficient to localise point sources and that regularisers such as total variation are not required in the nonnegative setting.

TL;DR: In this article, landmark diffusion maps (L-dMaps) are proposed to reduce the complexity of out-of-sample diffusion maps to O(M ), where M ≪ N is the number of landmark points selected using pruned spanning trees or k-medoids.

TL;DR: In this paper, it was shown that every frame which is norm-bounded below can be represented as a finite union of sequences { (T j ) n φ j } n = 0 ∞, j = 1, …, J for some bounded operators T j and elements φ J in the underlying Hilbert space.

TL;DR: In this article, the diffusion distance to a set B ⊂ V is defined as the smallest number of steps d B ( i ) ∈ N required for half of all random walks started in i and moving randomly with respect to the weights p i j to visit B within d B( i ) steps.

TL;DR: In this article, a rapid transformation between spherical harmonic expansions and their analogues in a bivariate Fourier series is derived, and the change of basis is described in two steps: first, expansions in normalized associated Legendre functions of all orders are converted to those of order zero and one; then, these intermediate expressions are re-expanded in trigonometric form.

TL;DR: In this article, the authors constructed a new infinite family of complex equiangular tight frame operators from abelian generalized quadrangles and vice versa, and proved the existence of certain generalized quadraids.

TL;DR: In this article, a joint multifractal analysis of a collection of signals unravels correlations between the locations of their pointwise singularities using multivariate multiresolution quantities, and a framework which allows to estimate joint multirefractal spectra is presented.

TL;DR: This paper investigates the complex gradient descent method (CGD) for the best rational approximation of a given order to a function in the Hardy space on the unit disk and employs a fast search algorithm to find the initial, then finds the target poles by gradient descent optimization.

TL;DR: The computational complexities of the resulting FFT algorithms are analyzed, that exploits the structure of the suggested multiple rank-1 lattice spatial discretizations, in detail and obtain upper bounds in O ( M log ⁡ M ) , where the constants depend only linearly on the spatial dimension.

TL;DR: It is illustrated that the continuity of linear functionals, used to obtain the non-point-evaluation functional data, on an FRKHS is necessary for the stability of the numerical reconstruction algorithm using the data.

TL;DR: In this paper, the stability of the Gabor transform was shown to scale at least quadratically exponentially in the dimension of the subspaces of the signal domain L 2 (R ).

TL;DR: In this paper, the spectral sparsity of the point source models as well as the incoherence between point spread functions is exploited to identify the membership and locations of point sources that are convolved with different band-limited point spread function.

TL;DR: In this paper, the authors introduce diffusion Frechet functions and diffusion diffusion vectors associated with probability distributions on Euclidean space and the vertex set of a weighted network, respectively, and prove that these functional statistics are stable with respect to the Wasserstein distance between probability measures.

TL;DR: In this article, the authors investigated the solution of boundary value problems on polygonal domains for elliptic partial differential equations and showed that the solutions near corners are representable, to arbitrary order, by linear combinations of certain non-integer powers and noninteger powers multiplied by logarithms.

TL;DR: In this article, the authors studied the underlying combinatorial structures of harmonic BTFs and showed that if a harmonic frame is generated by a divisible difference set, a partial difference set or by a special structure with certain Gauss summing properties, all three of which are generalizations of difference sets that fall under the umbrella term "bidifference set", then it is either a BTF or an ETF.

TL;DR: A new approximate multiresolution analysis using a single Gaussian as the scaling function, which is called Gaussian MRA (GMRA), which achieves accuracies beyond the reach of MC but also produces a PDF expressed as a Gaussian mixture, thus allowing for further efficient computations.

TL;DR: In this paper, the authors studied the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired non-uniformly, i.e., not necessarily on a uniform Cartesian grid.

TL;DR: This paper builds up a framework for almost everywhere matrix recovery and uses the tools from algebraic geometry to study the question and present some results to address it under many different settings.

TL;DR: In this paper, a family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales is presented, where the representation coefficients are obtained as inner products with the elements of a continuously indexed family of timefrequency atoms.

TL;DR: The proposed estimator relies on the formalism of smoothing in reproducing kernel Hilbert spaces and the choice of an appropriate regularization term that takes the smoothness of the operator into account, and is numerically tractable in very large dimensions.

TL;DR: In this article, the authors consider the worst case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors x ∈ C d (up to a single global phase multiple) from the magnitudes of shifted local correlation measurements.