Numerical weather prediction requires the determination of the initial state of the system. Indeed, the true state, at a given moment and in all points of space, is not accessible. In order to retrieve an optimal initial condition one uses the so called data assimilation methods that combine information from observations, model equations and their respective error statistics. Since the late 70s, satellites are a dominant source of information. Errors associated to such data are highly correlated in space, which can be detrimental if this is not properly accounted for. However their density in space allows for the efficient use of multi-scale transformation, which in turn permit a cheap but good approximation of said error statistics representation. The drawback of such approach is that the impact of missing data on the error statistics representation may not be trivial. The aim of this paper is to propose solutions to overcome the problem of missing data (without introducing more signal, e.g. through inpainting, which would cause even more statistical problems) when representing the noise properties in a wavelet space.