Hopfield Neural Network deconvolution for weak lensing measurement
  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.
