Showing papers in "Applied and Computational Harmonic Analysis in 2013"

TL;DR: The spectral CS (SCS) recovery framework for arbitrary frequencysparse signals is introduced and it is demonstrated that SCS signicantly outperforms current state-of-the-art CS algorithms based on the DFT while providing provable bounds on the number of measurements required for stable recovery.

TL;DR: In this article, the authors take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one, and propose effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior.

TL;DR: In this paper, a sharp condition on the restricted isometry property (RIP) for both sparse signal recovery and low-rank matrix recovery was established for both low rank and high rank matrix recovery.

TL;DR: A nonlinear matching pursuit method is proposed by generalizing the classical matching pursuit for the l^0 optimization problem and it can be implemented very efficiently and is very stable to noise.

TL;DR: In this paper, the authors proposed the use of the sparse regularization technique in combination with curvelets, which gives rise to an edge-preserving reconstruction, and showed that the dimension of the problem can be significantly reduced in the curvelet domain.

TL;DR: In this paper, the authors considered a class of functions composed of waveforms that repeat nearly periodically, and for which the instantaneous frequency can be given a rigorous meaning, and they showed that Synchrosqueezing can be used to determine instantaneous frequency of functions in this class, even if the waveform is not harmonic, thus generalizing earlier results for cosine wave functions.

TL;DR: In this paper, the authors established a lower bound on the mean-squared error, which holds regardless of sensing/design matrix being used and regardless of the estimation procedure, and this lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an l 1 estimation procedure such as the Dantzig selector.

TL;DR: In this paper, modified variants of the sparse Fourier transform algorithms from Iwen (2010) are presented which improve on the approximation error bounds of the original algorithms. And simple methods for extending the improved Fourier transforms to higher dimensional settings are developed, which will identify a near-optimal k-term Fourier series for any given input function.

TL;DR: It is shown that for a special class of signals it is possible to recover the initial state using a reduced number of measuring devices activated more frequently.

TL;DR: In this article, an integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions, and the capacitance of the unit cube is determined with unprecedented accuracy.

TL;DR: In this paper, the authors consider a Borel probability measure with compact support and show that it admits an exponential Riesz basis but no exponential orthonormal basis, and they construct a class of singularly continuous continuous measures that have an exponential-Riesz-based basis, which is the first such kind of examples.

TL;DR: In this article, the authors introduce the notion of spline functions in geometrically doubling quasi-metric spaces, which have interpolation and reproducing properties as the linear splines in Euclidean spaces.

TL;DR: A multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nystrom interpolation method.

TL;DR: A new fast algorithm for computing the spectrum of an N × N symmetric tridiagonal matrix in O ( N ln N ) operations is proposed, providing for a comparison with existing techniques in terms of running time and accuracy.

TL;DR: This paper applies concentration techniques with l 2 -empirical covering numbers to present an elaborate capacity dependent analysis for the algorithm, which yields shaper estimates in both confidence estimation and convergence rate.

TL;DR: A systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis and an explicit medical imaging application is introduced.

TL;DR: In this paper, a sharpening of the notion of fusion frames is introduced, called tight fusion frames, which enable signal decompositions into weighted linear subspace components and are closely related to the classical notions of designs and cubature formulas in Grassmann spaces.

TL;DR: In this paper, it is proved that by using alternate duals, we obtain more accurate results than using Canonical duals in Gabor frame theory, where the duals enable us to write every element in the underlying Hilbert space as a linear combination of the frame elements.

TL;DR: In this paper, the authors construct Banach spaces of functions on an input space X with the following properties: (1) B possesses an l 1 norm in the sense that B is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; point evaluations are continuous linear functionals on B and are representable through a bilinear form with a kernel function; and (2) regularized learning schemes on B satisfy the linear representer theorem.

TL;DR: In this article, the authors obtain necessary and sufficient conditions for the admissible vectors of a new unitary non-irreducible representation U, which generalizes the restriction of the metaplectic representation to triangular subgroups.

TL;DR: In this article, a simple algorithm for the construction of tight framelet filter banks with symmetry and two high-pass filters has been proposed, which allows us to obtain a wider class of tight wavelet frames with symmetry which are not available in the current literature.

TL;DR: In this paper, the authors extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space X into Cn, and show that X has a second countable topology with respect to which the eigenfunctions are continuous and such that the series representing K uniformly converges to K on compact subsets of X×X, provided that the support of μ is X.

TL;DR: In this paper, the authors consider the problem of finding the optimal completions of a set of matrices that minimize submajorization on sets that are naturally associated with the problems above.

TL;DR: In this paper, an analysis sparsity prior is proposed to regularize an ill-posed inverse problem, where the objective is the sum of a quadratic data fidelity term and a regularization term formed of the L 1-norm of the correlations between the sought after signal and atoms in a given (generally overcomplete) dictionary.

TL;DR: In this paper, it was shown that in any separable Hilbert space, any pair of Bessel sequences can be extended to a pair of dual frames, and that the generator of the added Gabor Bessel sequence can be compactly supported as well.

TL;DR: In this paper, theoretical and practical anisotropic nonlocal means (ANLM) algorithms are introduced and proved that they are near minimax optimal for edge-dominated images from the Horizon class, and an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

TL;DR: It is established that sampling with well-localized frames improves both the accuracy of the numerical frame approximation as well as the robustness and efficiency of the (finite) frame operator inversion.

TL;DR: Four TFD algorithms to minimise both the computation and memory loads are presented, optimised for a specific kernel category.

TL;DR: A variation of the soft-thresholding algorithm for finding sparse approximate solutions of the equation A x = b, where as the sparsity of the iterate increases the penalty function changes, leading to a significant reduction of the total number of iterations.