Wavelet Helmholtz decomposition for weak lensing mass map reconstruction
  To derive the convergence field from the gravitational shear (gamma) of the
background galaxy images, the classical methods require a convolution of the
shear to be performed over the entire sky, usually expressed thanks to the Fast
Fourier transform (FFT). However, it is not optimal for an imperfect geometry
survey. Furthermore, FFT implicitly uses periodic conditions that introduce
errors to the reconstruction. A method has been proposed that relies on
computation of an intermediate field u that combines the derivatives of gamma
and on convolution with a Green kernel. In this paper, we study the wavelet
Helmholtz decomposition as a new approach to reconstructing the dark matter
mass map. We show that a link exists between the Helmholtz decomposition and
the E/B mode separation. We introduce a new wavelet construction, that has a
property that gives us more flexibility in handling the border problem, and we
propose a new method of reconstructing the dark matter mass map in the wavelet
space. A set of experiments based on noise-free images illustrates that this
Wavelet Helmholtz decomposition reconstructs the borders better than all other
existing methods.
