Summary: We first introduce a similarity assumption to describe the similarity phenomenon in natural images, and establish a similarity principle which supplies a simple mathematical justification for the non-local means filter in removing Gaussian noises. Using the similarity principle in an adapted way, we then propose a new algorithm, called mixed noise filter (MNF), to remove simultaneously a mixture of Gaussian and random impulse noises. Our experiments show that our new filter improves significantly the trilateral filter in removing mixed noises, and that it is as efficient as the non-local means filter in removing Gaussian noises, and as good as the trilateral filter in removing random impulse noises.