Super-Resolution with Noisy Measurements: Reconciling Upper and Lower Bounds

Qiao, Heng; Shahsavari, Sina; Pal, Piya

doi:10.1109/icassp40776.2020.9054159

Cited by 3 publications

(1 citation statement)

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“…Super-resolution imaging, on the other hand, pertains to recovering finer details of an unknown signal from low resolution measurements. Despite recent advances in the development of convex algorithms and theoretical guarantees for super-resolution [17][18][19][20][21][22][23], most existing methods obey the so-called Rayleigh resolution limit (especially in presence of noise), which strictly speaking, may defeat the purpose of super-resolution. Furthermore, Signal-to-Noise Ratio (SNR) is a primary concern in many super-resolution imaging problems, especially in photon-limited optical imaging.…”

Section: Introductionmentioning

confidence: 99%

Fundamental Trade-Offs in Noisy Super-Resolution with Synthetic Apertures

Shahsavari

Millhiser

Pal

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper concerns understanding the fundamental performance benefits of co-array based super-resolution techniques in low SNR settings. Proper sensor placement in the form of a sparse nested array allows the generation of difference co-arrays with large virtual apertures that offer higher resolution. However, the performance of super-resolution aperture synthesis techniques is known to degrade in presence of large noise levels. The main contribution of this paper is to rigorously establish that nested arrays provide lower Cramér-Rao bounds than a ULA (with the same number of sensors) in the low SNR regime, and therefore can lead to better resolvability of closely spaced sources. Numerical experiments are performed to validate theoretical claims, including demonstration of MUSIC spectra with two closely-spaced sources using ULA and nested arrays in various SNR settings. 1

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