Showing papers in "Applied and Computational Harmonic Analysis in 2018"

TL;DR: In this paper, a sparsely-connected depth-4 neural network is constructed to approximate a function f on a d-dimensional manifold and bound its error in approximating f. The size of the network depends on the dimension and curvature of the manifold.

TL;DR: In this paper, the problem of sampling k-bandlimited signals on graphs is studied and two sampling strategies are proposed: one is non-adaptive and the other is adaptive but yields optimal results.

TL;DR: In this article, the authors consider clustering of point clouds obtained as samples of a ground-truth measure and obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for spectral convergence to hold.

TL;DR: This work proposes an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections, and constructs a more parsimonious embedding using only the eigenvectors corresponding to unique eigends, and shows that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance.

TL;DR: The block orthogonal matching pursuit algorithm is used to recover block sparse signals from measurements $\y=\A\x+\v$, where $\v$ is an $\ell_2$-bounded noise vector for some constant $\epsilon$ and some sufficient conditions based on the block restricted isometry property (block-RIP) are investigated.

TL;DR: In this paper, the root-exponential decay in the reconstruction error due to quantization was shown for arbitrary signals, including compressible ones, and account for measurement noise, and the results hold for sub-Gaussian (including Gaussian and Bernoulli) random compressed sensing measurements.

TL;DR: In this article, the Cumulative Distribution Transform (CDT) is proposed for pattern representation that interprets patterns as probability density functions, and has special properties with regards to classification.

TL;DR: In this paper, the statistical properties of compactly supported synchrosqueezed transforms for wave-like components embedded in a generalized Gaussian random process in multidimensional spaces are investigated.

TL;DR: In this paper, it was shown that these properties also hold for directional scale-discretised wavelets on the sphere and derive similar localisation and uncorrelation bounds in both the scalar and spin settings.

TL;DR: A fast randomized algorithm that computes a low rank LU decomposition using random projections type techniques and recent results from random matrix theory related to subgaussian matrices are used.

TL;DR: In this paper, it was shown that 4 n r − 4 r 2 generic measurements are both necessary and sufficient for the recovery of rank-r matrices in C n × n.

TL;DR: In this article, the authors proposed a time-frequency analysis method based on the adaptive harmonic model and applied FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) to achieve an efficient numerical approximation of the functional.

TL;DR: A new definition of distance between points on two spaces is introduced, localized kernels based on the two spaces and certain interaction parameters are constructed, and the evolution of smoothness of a function on one space to its lifting to the other space via the landmarks is studied.

TL;DR: In this article, a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion is presented and analyzed; the theoretical analysis of the method under the LCCM model is provided.

TL;DR: In this article, the centroid-symmetric real equiangular tight frame (ETF) constructions were studied and proved to have centroidal symmetry about their centroid.

TL;DR: In this paper, the authors give an unconditional basis of H at 1 ( X ) and several equivalent characterizations of the Hardy space in terms of wavelets, which are proved useful.

TL;DR: A kernel-based regression algorithm with the C-loss and l 1 -regularizer in data dependent hypothesis spaces is investigated, establishing the asymptotic learning rate and sparsity characterization of the derived predictor.

TL;DR: Effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs are introduced.

TL;DR: In this article, the wave-front set of the Born-Jordan distribution has been studied for general signals in L 2 and, more in general, in the space of temperate distributions.

TL;DR: In this paper, the sufficient condition in terms of the RIC and ROC for the stable and robust recovery of signals in both noiseless and noisy settings was established via weighted l 1 minimization when there is partial prior information on support of signals.

TL;DR: In this paper, it was shown that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products and the tensor product of a standard wavelet representation with a wavelet-like representation.

TL;DR: Characterizations of the tightness of a sequence of framelet systems for $L_{2}(\mathcal{M})$ in both the continuous and semi-discrete settings are provided and fast framelet filter bank transforms on $M$ are shown to be realizable with nearly linear computational complexity.

TL;DR: In this article, the Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask, and the uniqueness of projected fixed point is proved and for setting 2) the local geometric convergence is derived with a rate given by a spectral gap condition.

TL;DR: Magnetic Eigenmaps as discussed by the authors is a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called magnetic eigenmaps.

TL;DR: In this article, the authors generalize the theory of local kernels to represent degenerate mappings where the intrinsic dimension of the data set is higher than the intrinsic dimensions of the feature space, and they present a rigorous method with asymptotic error bounds for estimating D H from the training data set and feature values.

TL;DR: In this paper, the authors identify one of the sources of the dimensional term and exploit this insight to develop sharper matrix concentration inequalities, which use information beyond the matrix variance to improve the dimensional dependence.

TL;DR: In this article, a sharp version of the Balian low theorem for the generators of finitely generated shift-invariant spaces is proven for the generator f k = 1 K ⊂ L 2 (R d ) with extra invariance by a suitable finer lattice.

TL;DR: It is proved that with an almost self-located robust frame, any signal except from a Lebesgue measure zero subset can be recovered from its unordered partial frame coefficients, and it is proposed that any randomly generated frame is almost surely self- located robust.

TL;DR: The multidimensional butterfly factorization as discussed by the authors is a data-sparse representation of multi-dimensional kernel matrices that satisfy the complementary low-rank property, and it can be computed in O(n) time.

TL;DR: An algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime based on the recent observation that the solutions of equations of this type can be accurately represented using nonoscillatories phase functions is described.