A neural network-based method for speckle removal in synthetic aperture radar (SAR) images is introduced. The method rests on the idea that a neural network learning machine, trained on artificially generated input-target couples, can be used to efficiently process real SAR data. The explicit plus-point of the method is that it is trained with artificially generated data, reducing the demands put on real input data such as data quality, availability and cost price. The artificial data can be generated in such a way that they fit the particular characteristics of the images to be denoised, yielding case-specific, high-performing despeckling filters. Acomparative study with three classical denoising techniques (Enhanced Frost (EF), Enhanced Lee (EL) and GammaMAP (GM)) and a wavelet filter demonstrated a superior speckle removal performance of the proposed method in terms of quantitative performance measures. Moreover, qualitative evaluation of the despeckled results was in favour of the proposed method, confirming its speckle removal efficiency.