Supervised learning with recurrent neural networks has been used to estimate perturbations that adversely affect image quality of natural guide stars due to atmospheric turbulence. While this method has been shown to be effective for generating spatially variant point spread functions (PSFs) for image reconstruction using low-turbulence models, recent extensions to these methods, facilitated by enhancements to optimize network parameters, show potential to extend this method to moderate-turbulence multilayer models. In this paper, spatio-temporal learning using reservoir computing, a discriminative learning method known as an echo state network, is proposed to estimate the spatially variant PSF, thus allowing for improved image restoration of point-source exo-atmospheric objects outside the isoplanatic patch. The forward problem is modelled by training a reservoir computer with time-series perturbations from three or more natural guide stars. Known site profile data is incorporated to optimize the model for training, where perturbations under similar conditions are used to test estimated aberrations over a wide, anisoplanatic field.
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23 August 2018: A typographical correction was made to paragraph 4 in section 4.
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