Scrape-off layer (SOL) and edge plasma turbulence contribute significantly to the radial particle and heat transport lowering plasma confinement and increasing heat load on the plasma facing components. SOL turbulence is predominantly intermittent which manifest in the occurrence of isolated density filaments or blobs. Filaments propagate radially outwards towards plasma facing components limiting their lifetime by erosion and sputtering. To characterize this phenomenon in detail few diagnostic techniques are available. Beam emission spectroscopy is a diagnostic capable of measuring plasma turbulence in both SOL and edge plasmas. Due to the finite lifetime of the excitation states during the beam - plasma interaction, and the misalignment between the optics and the magnetic field, spatial smearing is introduced in the measurement. In this paper a novel method is introduced to overcome this hindering effect by inverting the fluctuation response matrix on an optimally smoothed signal. We show that this method is fast and provides significantly more accurate absolute density fluctuation reconstruction than the direct inversion technique. The presented method is usable for all types of beam emission diagnostics where the spatial resolution is higher than the combined smearing of the atomic physics and the observation.