Related papers: Constructing curvelet-like bases and low-redundanc…
This paper introduces the synchrosqueezed curvelet transform as an optimal tool for 2D mode decomposition of wavefronts or banded wave-like components. The synchrosqueezed curvelet transform consists of a generalized curvelet transform with…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
The main contribution of this paper is a constructive method for building separable multivariate vector-valued wavelet bases in the general framework of \( L^2(\mathbb{R}^d, \mathbb{R}^m) \) for any \( d, m \geq 1 \). While separable…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
Informed by LES data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic, and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract…
In this paper, we construct wavelet tight frames with n vanishing moments for Dubuc-Deslauriers 2npoint semi-regular interpolatory subdivision schemes. Our motivation for this construction is its practical use for further regularity…
This thesis is a study of large sets of unit vectors in $\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the maximal size of a set of lines with only…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
Hyperspectral data consists of large number of features which require sophisticated analysis to be extracted. A popular approach to reduce computational cost, facilitate information representation and accelerate knowledge discovery is to…
We develop a method to design tunable quasiperiodic structures of particles suspended in a fluid by controlling standing acoustic waves. One application of our results is to ultrasound directed self-assembly, which allows fabricating…
Large antenna arrays can be used to generate highly focused beams that support very high data rates and reduced energy consumption. However, optimal beam focusing requires large amount of feedback from the users in order to choose the best…
We introduce a general framework for the construction of polynomial frames in $L^2(\mathbb{S}^{d-1})$, $d \geq 3$, where the frame functions are obtained as rotated versions of an initial sequence of polynomials $\Psi^j$, $j\in…
Existing beamforming-based full-duplex solutions for multi-antenna wireless systems often rely on explicit estimation of the self-interference channel. The pilot overhead of such estimation, however, can be prohibitively high in…
Bandpass filtering techniques are widely used in spectroscopy. However, conventional symmetric-padding filtering methods introduce boundary artifacts that distort the signal at the edges. We present a rubber band filter: a robust method for…
It was proposed that a flat silver layer could be used to form a sub-diffraction limited image when illuminated near its surface plasmon resonance frequency [J. B. Pendry, Phys. Rev. Lett. 86, 3966 (2000)]. In this paper, we study the…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
Compression at low bitrates in modern codecs often introduces banding artifacts, especially in smooth regions such as skies. These artifacts degrade visual quality and are common in user-generated content due to repeated transcoding. We…
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data.…
Enabled by x-ray free-electron lasers, nonlinear optical phenomena can be explored in the x-ray domain nowadays. Among the multitude of newly accessible processes, this theoretical study focuses parametric x-ray optical wavemixing for…