Abstract
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is shown that the probabilities increase to one when the sample size increases. Further, explicit reconstruction formulae for signals in these subsets have been obtained for which the numerical simulations have also been performed.
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Acknowledgements
The first named author S. Arati acknowledges the financial support of the National Board for Higher Mathematics, Department of Atomic Energy (Government of India). The second named author P. Devaraj acknowledges the financial support of the Department of Science and Technology (Government of India) under DST-SERB Research Grant MTR/2018/000559. The authors thank the reviewers for their valuable comments.
Funding
Funding was provided by National Board for Higher Mathematics (NBHM) and Science and Engineering Research Board, Department of Science and Technology(DST-SERB), Government of India.
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Arati, S., Devaraj, P. & Garg, A.K. Random Average Sampling and Reconstruction in Shift-Invariant Subspaces of Mixed Lebesgue Spaces. Results Math 77, 223 (2022). https://doi.org/10.1007/s00025-022-01738-w
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DOI: https://doi.org/10.1007/s00025-022-01738-w
Keywords
- Mixed Lebesgue spaces
- probabilistic reconstruction
- random average sampling
- sampling inequality
- shift-invariant subspaces