15 October 2012 Quantum limits of super-resolution via sparsity constraint
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Abstract
Sparsity constraint is a priori knowledge of the signal, which means that in some properly chosen basis only a small percentage of the signal components is nonzero. Sparsity constraint has been used in signal and image processing for a long time. Recent publications have shown that by taking advantage of the Sparsity constraint of the object, super-resolution beyond the diffraction limit could be realized. In this paper we present the quantum limits of super-resolution for the sparse objects. The key idea of our paper is to use the discrete prolate spheroidal sequences (DPSS) as the sensing basis. We demonstrate both analytically and numerically that this sensing basis gives superior performance over the Fourier basis conventionally used for sensing of sparse signals. The explanation of this phenomenon is in the fact that the DPSS are the eigenfunctions of the optical imaging system while the Fourier basis are not. We investigate the role of the quantum fluctuations of the light illuminating the object, in the performance of reconstruction algorithm. This analysis allows us to formulate the criteria for stable reconstruction of sparse objects with super-resolution.
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Hui Wang, Hui Wang, Shensheng Han, Shensheng Han, Mikhail I. Kolobov, Mikhail I. Kolobov, } "Quantum limits of super-resolution via sparsity constraint", Proc. SPIE 8518, Quantum Communications and Quantum Imaging X, 85180P (15 October 2012); doi: 10.1117/12.928842; https://doi.org/10.1117/12.928842
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