201. Nonuniform Sampling in L p -Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform.
- Author
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Jiang, Yingchun and Yang, Jing
- Subjects
- *
IRREGULAR sampling (Signal processing) , *FOURIER transforms , *FUNCTION spaces , *ALGORITHMS , *KRYLOV subspace - Abstract
In this paper, the sampling and reconstruction problems in function subspaces of L p (R n) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval's relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the L p -stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a L p -subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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