Wavelet Helmholtz decomposition for weak lensing mass map reconstruction

Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, SEDI-SAP, Service d’Astrophysique, CEA Saclay, F-91191GIF-Sur-YVETTE CEDEX, FranceJanuary 26, 2012Abstract To derive the convergence eld from the gravitational shear of the background galaxy images, theclassical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanksto 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 proposedthat relies on computation of an intermediate eld uthat combines the derivatives of and on convolution with aGreen kernel. In this paper, we study the wavelet Helmholtz decomposition as a new approach to reconstructingthe dark matter mass map. We show that a link exists between the Helmholtz decomposition and the E/B modeseparation. We introduce a new wavelet construction, that has a property that gives us more exibility in handlingthe border problem, and we propose a new method of reconstructing the dark matter mass map in the waveletspace. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz decompositionreconstructs the borders better than all other existing methods.