  Multiplicative noise widely exists in radar images, medical images and other
important fields' images. Compared to normal noises, multiplicative noise has a
generally stronger effect on the visual expression of images. Aiming at the
denoising problem of multiplicative noise, we linearize the nonlocal means
algorithm with deep learning and propose a linear attention mechanism based
deep nonlocal means filtering (LDNLM). Starting from the traditional nonlocal
means filtering, we employ deep channel convolution neural networks to extract
the information of the neighborhood matrix and obtain representation vectors of
every pixel. Then we replace the similarity calculation and weighted averaging
processes with the inner operations of the attention mechanism. To reduce the
computational overhead, through the formula of similarity calculation and
weighted averaging, we derive a nonlocal filter with linear complexity.
Experiments on both simulated and real multiplicative noise demonstrate that
the LDNLM is more competitive compared with the state-of-the-art methods.
Additionally, we prove that the LDNLM possesses interpretability close to
traditional NLM.
