Abstract: To address the problem of high time consumption of the affine non-local mean (ANLM) algorithm in the denoising process, a fast affine non-local mean denoising (F-ANLM) algorithm was proposed. Through time analysis of the affine non-local mean algorithm, it was known that the two modules, the affine transformation and the calculation of the affine invariant similarity measure, were the most time-consuming. Therefore, the optimization strategy was proposed from these tworegards. The algorithm first employed the included angle of the feature vector of the affine covariant structure tensor instead of the main direction of the SIFT operator, and then rewrote the affine invariant similarity measure in the ANLM method into the form of discrete convolution. In addition, the Fast Fourier Transform was adopted to reduce the amount of convolution operation and accelerate the calculation of similarity measures between affine covariant feature regions. Experiments show that the F-ANLM algorithm can simplify the calculation of affine transformation and affine invariant similarity measures, and greatly increase the speed compared with the original ANLM algorithm. 

Key words: non-local, structure-tensor, affine-invariant, convolution, similarity-measure, Fast-Fourier