Showing papers in "Applied and Computational Harmonic Analysis in 2011"

TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.

TL;DR: A novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph using the spectral decomposition of the discrete graph Laplacian L, based on defining scaling using the graph analogue of the Fourier domain.

TL;DR: A condition on the measurement/sensing matrix is introduced, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries.

TL;DR: An efficient recovery algorithm for the unknown angles from the top eigenvector of a specially designed Hermitian matrix is introduced and extensions of the eigen vector method are presented to other synchronization problems that involve different group structures and their applications, such as the time synchronization problem in distributed networks.

TL;DR: In this article, the authors presented a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying A T to a collection of l random vectors, where l is an integer equal to or slightly greater than k; the scheme is efficient whenever A and A T can be applied rapidly to arbitrary vectors.

TL;DR: A series of computational experiments indicate that the signal acquisi- tion error is minimized when a significant fraction of the CS measurements is allowed to saturate, challenging the conventional wisdom of both conventional sampling and CS.

TL;DR: The sufficient condition for restricted isometry constants has been improved to δ 2 k 0.4931 for general k and also, in some special cases, the sufficient condition can be improved to £2.6569 .

TL;DR: In this paper, the projected generalized Stein Unbiased Risk Estimator (GSURE) is used to determine the threshold value λ and the iterations number K in iterative shrinkage methods for image deblurring and image zooming.

TL;DR: This paper applies concentration techniques with l2-empirical covering numbers to improve the learning rates for the algorithm and shows that a function space involved in the error analysis induced by the l1-regularizer and non-symmetric kernel has nice behaviors in terms of the l2,000,000 covering numbers of its unit ball.

TL;DR: This work completely resolve the question of existence of tight fusion frames in the special case where the underlying space is finite-dimensional and the fusion frame's subspaces have equal dimension.

TL;DR: This paper provides a mathematical foundation for the least square regression learning with indefinite kernel and coefficient regularization and deduce the error bound and prove the asymptotic convergence.

TL;DR: In this article, a null space property for the uniqueness of the sparse solution vectors recovered from a minimization in l p quasi-norm subject to multiple systems of linear equations, where p ∈ ( 0, 1 ], was shown.

TL;DR: In this article, a method to stably approximate the inverse of the noisy Radon transform on the rotation group SO (3 ) is proposed. But the performance of the finally obtained iterative approximation is studied through several experiments.

TL;DR: The distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if they are isometric when endowed with geodesic distances.

TL;DR: This framework implies that, according to the best available analysis on three state-of-the-art greedy algorithms, IHT requires the fewest number of compressed sensing measurements, has the best proven stability bounds, and has the lowest per iteration computational cost.

TL;DR: This work introduces an algorithm that determines the orientability of the intrinsic manifold given a sufficiently large number of sampled data points and provides an alternative procedure for computing the eigenfunctions of the Laplacian that are important in the diffusion map framework for reducing the dimensionality of the data.

TL;DR: In this paper, the 3-dimensional continuous shearlet transform has been used to characterize the boundary set of solid regions in R 3 by identifying both its location and local orientation.

TL;DR: In this paper, the authors define frames in a Banach space as a collection of elements in B by making use of semi-inner products and establish the Shannon sampling theorem in Banach spaces.

TL;DR: In this article, an abstract framework for the construction of Banach spaces of distributions from group representations is presented, which relies on duality arguments, which are often verifiable in cases where integrability fails.

TL;DR: In this paper, a wide class of MRA-based wavelet systems which are not frames in L2(R d ), generally speaking, was studied and their approximation order was investigated.

TL;DR: In this article, a multivariate Gabor frame with a Gaussian window was proposed, which is equivalent to a sampling problem in Bargmann-Fock space in higher dimensions.

TL;DR: This paper investigates the consistency of the regularized spectral clustering algorithm, which has been proposed recently, and establishes a convergence rate that depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers.

TL;DR: In this paper, the Pontryagin duality was used to describe the unitary equivalence classes of harmonic frames, and it was shown that all harmonic frames of n vectors for C d can be constructed from d-element subsets of G ( | G | = n ).

TL;DR: The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which are coined upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space.

TL;DR: In this paper, a constrained approximation technique is used to recover solutions to elliptic partial differential equations from incomplete and corrupted boundary data, which involves the use of generalized Hardy spaces of functions whose real and imaginary parts are related by formulae similar to the Cauchy-Riemann equations.

TL;DR: In this paper, a vector is encoded using a permutation source code to quantize its frame expansion and the encoding is a partial ordering of the frame expansion coefficients, which produces a greater number of possible quantization rates and higher maximum rate.

TL;DR: In this paper, the authors consider the time-frequency localization of the generator of a principal shift-invariant space on the real line which has additional shift invariance, and prove that if the generator is not translation invariant, then any of its orthonormal generators is non-integrable.

TL;DR: Compared to existing differentiation schemes based on orthogonal polynomials, the new class of differentiation schemes requires fewer points per wavelength to achieve the same accuracy when it is used to approximate derivatives of bandlimited functions.

TL;DR: This work builds a new biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, and uses both pairs to construct isotropic or anisotropic divergence-free wavelet bases on the hypercube.

TL;DR: In this paper, a systematic study on tight periodic wavelet frames and their approximation orders is conducted, where a necessary and sufficient condition, in terms of refinement masks, for applying the unitary extension principle for periodic functions to construct tight wavelet frame is identified.