In this paper, a novel method for the quality assessment of despeckled SAR images is proposed. This method is based on the observation that the perceived quality of despeckled SAR images is not always appropriately described by classical statistical and deterministic parameters that are proposed in the literature. Various evaluations are performed here. A preliminary visual qualitative evaluation is taken as a reference for the subsequent quantitative assessment. Then, a revised statistical analysis that can solve some of the drawbacks of previous methods is proposed; however, the statistical approach still has certain drawbacks. To address this problem, a new frequency analysis approach is first proposed, together with a definition of the appropriate indexes. In this way, it is possible to select the best filter in terms of noise reduction, edge and texture preservation, while limiting the effect of introduced distortions. While statistical analysis is widely used in the literature, frequency analysis has never been presented for this aim, especially for non-linear filters. We prove that frequency analysis can robustly identify the best filter, taking perceptual considerations into account, even when statistical analysis fails. Despeckling methods based on anisotropic diffusion algorithms are used for a comparison, but the proposed analysis can be applied to any filtering method. Experiments are presented with SAR images from the Italian Cosmo/Skymed constellation. Both Stripmap and Spotlight acquisitions have been evaluated, and to prove the validity of the proposed method with respect to different spatial resolutions and different classes of interest, various classes are considered.