Hopfield Neural Network deconvolution for weak lensing measurement

TL;DR

This paper introduces a novel weak lensing shear measurement method using Hopfield Neural Network-based deconvolution of galaxy images, achieving high accuracy on simulated data.

Contribution

It presents the first use of full image deconvolution with Hopfield Neural Networks for weak lensing shear measurement, improving accuracy.

Findings

Achieved a quality factor of Q=87 on simulated data.

Biases on shear power spectrum are very low (+0.000009 additive, +0.0357 multiplicative).

Method outperforms previous approaches in simulated tests.

Abstract

Weak gravitational lensing has the potential to place tight constraints on the equation of the state of dark energy. However, this will only be possible if shear measurement methods can reach the required level of accuracy. We present a new method to measure the ellipticity of galaxies used in weak lensing surveys. The method makes use of direct deconvolution of the data by the total Point Spread Function (PSF). We adopt a linear algebra formalism that represents the PSF as a Toeplitz matrix. This allows us to solve the convolution equation by applying the Hopfield Neural Network iterative scheme. The ellipticity of galaxies in the deconvolved images are then measured using second order moments of the autocorrelation function of the images. To our knowledge, it is the first time full image deconvolution is used to measure weak lensing shear. We apply our method to the simulated weak lensing data proposed in the GREAT10 challenge and obtain a quality factor of Q=87. This result is obtained after applying image denoising to the data, prior to the deconvolution. The additive and multiplicative biases on the shear power spectrum are then +0.000009 and +0.0357, respectively.