Frame Bounds for Gabor Frames in Finite Dimensions

Palina Salanevich

doi:10.1109/SampTA45681.2019.9030964

Frame Bounds for Gabor Frames in Finite Dimensions

Palina Salanevich^*

^*Corresponding author for this work

University of California at Los Angeles

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

One of the key advantages of a frame compared to a basis is its redundancy. Provided we have a control on the frame bounds, this redundancy allows, among other things, to achieve robust reconstruction of a signal from its frame coefficients that are corrupted by noise, rounding error, or erasures. In this paper, we discuss frame bounds for Gabor frames (g, Λ) with generic frame set Λ and random window g. We show that, with high probability, such frames have frame bounds similar to the frame bounds of randomly generated frames with independent frame vectors.

Original language	English
Title of host publication	2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
Publisher	IEEE
ISBN (Electronic)	9781728137414
DOIs	https://doi.org/10.1109/SampTA45681.2019.9030964
Publication status	Published - 1 Aug 2019
Externally published	Yes
Event	13th International Conference on Sampling Theory and Applications, SampTA 2019 - Bordeaux, France Duration: 8 Jul 2019 → 12 Jul 2019

Conference

Conference	13th International Conference on Sampling Theory and Applications, SampTA 2019
Country/Territory	France
City	Bordeaux
Period	8/07/19 → 12/07/19

Keywords

Frequency modulation
Noise measurement
Redundancy
Robustness
Image reconstruction
Signal to noise ratio
Machine-to-machine communications
probability
signal reconstruction
vectors

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10.1109/SampTA45681.2019.9030964

Gabor_frame_boundsFinal published version, 311 KB

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title = "Frame Bounds for Gabor Frames in Finite Dimensions",

abstract = "One of the key advantages of a frame compared to a basis is its redundancy. Provided we have a control on the frame bounds, this redundancy allows, among other things, to achieve robust reconstruction of a signal from its frame coefficients that are corrupted by noise, rounding error, or erasures. In this paper, we discuss frame bounds for Gabor frames (g, Λ) with generic frame set Λ and random window g. We show that, with high probability, such frames have frame bounds similar to the frame bounds of randomly generated frames with independent frame vectors.",

keywords = "Frequency modulation, Noise measurement, Redundancy, Robustness, Image reconstruction, Signal to noise ratio, Machine-to-machine communications, probability, signal reconstruction, vectors",

author = "Palina Salanevich",

year = "2019",

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day = "1",

doi = "10.1109/SampTA45681.2019.9030964",

language = "English",

booktitle = "2019 13th International Conference on Sampling Theory and Applications, SampTA 2019",

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note = "13th International Conference on Sampling Theory and Applications, SampTA 2019 ; Conference date: 08-07-2019 Through 12-07-2019",

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AB - One of the key advantages of a frame compared to a basis is its redundancy. Provided we have a control on the frame bounds, this redundancy allows, among other things, to achieve robust reconstruction of a signal from its frame coefficients that are corrupted by noise, rounding error, or erasures. In this paper, we discuss frame bounds for Gabor frames (g, Λ) with generic frame set Λ and random window g. We show that, with high probability, such frames have frame bounds similar to the frame bounds of randomly generated frames with independent frame vectors.

KW - Frequency modulation

KW - Noise measurement

KW - Redundancy

KW - Robustness

KW - Image reconstruction

KW - Signal to noise ratio

KW - Machine-to-machine communications

KW - probability

KW - signal reconstruction

KW - vectors

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U2 - 10.1109/SampTA45681.2019.9030964

DO - 10.1109/SampTA45681.2019.9030964

M3 - Conference contribution

AN - SCOPUS:85082865387

BT - 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019

PB - IEEE

T2 - 13th International Conference on Sampling Theory and Applications, SampTA 2019

Y2 - 8 July 2019 through 12 July 2019

ER -

Frame Bounds for Gabor Frames in Finite Dimensions

Abstract

Conference

Keywords

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