Arian Maleki: March 13


Title: Minimax image denoising via anisotropic nonlocal means


Abstract: Image denoising is a fundamental primitive in image processing and computer vision. Denoising algorithms have evolved from the classical linear and median filters to more modern schemes like total variation denoising, wavelet thresholding, and bilateral filters. A particularly successful denoising scheme is the nonlocal means (NLM) algorithm, which estimates each pixel value as a weighted average of other, similar noisy pixels. I start my talk by proving that the popular nonlocal means (NLM) denoising algorithm does not "optimally" denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses in order to set its smoothing weights. In response, I introduce the anisotropic nonlocal means (ANLM) algorithm and prove that it is near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin, up to 2dB in mean square error.