Uncertainty Principles and Signal Recovery
Abstract
The uncertainty principle can easily be generalized to cases where the “sets of concentration” are not intervals. Such generalizations are presented for continuous and discrete-time functions, and for several measures of “concentration” (e.g., $L_2 $ and $L_1 $ measures). The generalizations explain interesting phenomena in signal recovery problems where there is an interplay of missing data, sparsity, and bandlimiting.
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Two mel-spectrograms of different time-frequency resolutions contain complementary information: one has better resolution along the time axis and the other has better resolution along the frequency axis.
“Since these two spectrograms contain complementary information-namely, one has a better resolution along the time axis and the other has a better resolution along the frequency axis”
From Speech Emotion Recognition with Dual-Sequence LSTM Architecture (2020) · cites this paper as [9]
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Speech Emotion Recognition with Dual-Sequence LSTM Architecture
Wang, J., Xue, M., Culhane, R., Diao, E., Ding, J., & Tarokh, V. (2020) · ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) · doi:10.1109/icassp40776.2020.9054629 · Cited by 162 · see citing works
Global and local uncertainty principles for signals on graphs
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- Authors
- Donoho, D. L., & Stark, P. B.
- Affiliations
- University of California, Berkeley (US)
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1989-06
- Volume
- 49
- Issue
- 3
- Pages
- 906-931
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2125455772
- Cited by
- 1,054
- References
- 32
- Citations by year
- 2026: 31 · 2025: 49 · 2024: 53 · 2023: 53 · 2022: 42 · 2021: 58 · 2020: 39 · 2019: 68 · 2018: 52 · 2017: 49 · 2016: 51 · 2015: 61 · 2014: 50 · 2013: 66 · 2012: 49
- FWCI
- 8.36
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Journal on Applied Mathematics (publishedVersion)
- UC Berkeley (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Keywords
- uncertainty principle, signal reconstruction, generalized uncertainty principle, concentration measures, missing data, sparsity, bandlimiting
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