Related papers: Frames adapted to a phase-space cover
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
The goal of this chapter is to review the recent work and advances in the area of space-time beamforming algorithms and their application to radar systems. These systems include phased-array \cite{melvin} and multi-input multi-output (MIMO)…
We propose an adaptive form of frameless rendering with the potential to dramatically increase rendering speed over conventional interactive rendering approaches. Without the rigid sampling patterns of framed renderers, sampling and…
Space-time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beam. The ability to manipulate and generate space-time distributions of light has been remarkably enhanced in past few…
We develop a geometrical framework that allows to obtain the electromagnetic field quantities in accelerated frames. The frame of arbitrary accelerated observers in space-time is defined by a suitable set of tetrad fields, whose timelike…
Many new types of sensing or imaging surfaces are based on periodic thin films. It is explained how the response of those surfaces to partially coherent fields can be fully characterized by a set of functions in the wavenumber spectrum…
Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…
An imaging system is proposed for matter-wave functions that is based on producing a quadratic phase modulation on the wavefunction of a charged particle, analogous to that produced by a space or time lens. The modulation is produced by…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
In dynamic acoustic environments with time-varying interferers, effective beamforming requires identifying stationary regions over time. The Capon beamformer, a whitened matched filter constrained to maintain unity gain in the desired…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations has led to limitations in the widely used conventional Fourier methods,…
We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary…
The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation and light-matter interaction. In particular, the transmission of customized electromagnetic fields is investigated for…
Metasurfaces allow tailored control over electromagnetic wavefronts. However, due to the local conservation of power flow, a passive, lossless, and reflectionless metasurface is limited to imparting phase discontinuities -- and not power…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…