Related papers: Nonstationary Gabor Frames - Approximately Dual Fr…
Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…
We show the existence of a family of frames of $L^2(\mathbb{R})$ which depend on a parameter $\alpha\in [0,1]$. If $\alpha=0$, we recover the usual Gabor frame, if $\alpha=1$ we obtain a frame system which is closely related to the so…
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…
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…
Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpful towards an explicit construction of such a frame, which…
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in…
We show the full structure of the frame set for the Gabor system $\mathcal{G}(g;\alpha,\beta):=\{e^{-2\pi i m\beta\cdot}g(\cdot-n\alpha):m,n\in\Bbb Z\}$ with the window being the Haar function $g=-\chi_{[-1/2,0)}+\chi_{[0,1/2)}$. The…
In recent work, redressed warped frames have been introduced for the analysis and synthesis of audio signals with non-uniform frequency and time resolutions. In these frames, the allocation of frequency bands or time intervals of the…
We study the phase reconstruction of signals $f$ belonging to complex Gaussian shift-invariant spaces $V^\infty(\varphi)$ from spectrogram measurements $|\mathcal{G} f(X)|$ where $\mathcal{G}$ is the Gabor transform and $X \subseteq…
One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly…
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these…
Reconstructing dynamic 3D scenes from monocular videos requires simultaneously capturing high-frequency appearance details and temporally continuous motion. Existing methods using single Gaussian primitives are limited by their low-pass…