Title: Sheer shear: weak lensing with one mode
The aim of this talk is to show the potential of the Karhunen-Loève (KL) decomposition in reducing the dimensionality of the data vector for cosmic shear measurements. This greatly simplifies the problem of computing covariance matrices. To do so, I shall first introduce the theoretical background of the KL decomposition. After a brief description of the CFHTLenS data we are using, I will focus on the method adopted to calculate the lensing power spectra and estimate the covariance matrix. Finally, I will discuss the constraints obtained on cosmological parameters after a KL compression and what are the potential limits of this method.