Related papers: Frames adapted to a phase-space cover
In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction.…
The so-called "flat optics" that shapes the phase of an incident wave in free space through subwavelength structures has a venerable history. In that domain, achieving high efficiency at large deflection angles requires a low absorption…
We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and…
This paper is concerned with the characterization of $\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation…
We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that…
We propose scene-adaptive strategies to efficiently allocate representation capacity for generating immersive experiences of indoor environments from incomplete observations. Indoor scenes with multiple rooms often exhibit irregular layouts…
A general technique for synthesizing both planar and conformal beamforming metasurfaces is presented that utilizes full-wave modeling techniques and rapid optimization methods. The synthesized metasurfaces consist of a patterned metallic…
Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
The diffraction of electromagnetic waves by screens (apertures in screens) with time-varying dimensions is studied. The generalized vector Kirchhoff's representation for this case is obtained. It is also shown that with accuracy up to the…
A body $\Theta$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary…
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…
Passive acoustic mapping enables the spatial mapping and temporal monitoring of cavitation activity, playing a crucial role in therapeutic ultrasound applications. Most conventional beamforming methods, whether implemented in the time or…
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
We study the problem of actively imaging a range-limited far-field scene using an antenna array. We describe how the range limit imposes structure in the measurements across multiple wavelengths. This structure allows us to introduce a…
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…