Feature-Preserving Noise Removal

Conventional image restoration algorithms use transform-domain filters, which separate the noise from the sparse signal among the transform components or apply spatial smoothing filters in real space whose design relies on prior assumptions about the noise statistics. These filters also reduce the information content of the image by suppressing spatial frequencies or by recognizing only a limited set of shapes. Here we show that denoising can be efficiently done using a nonlinear filter, which operates along patch neighborhoods and multiple copies of the original image. The use of patches enables the algorithm to account for spatial correlations in the random field whereas the multiple copies are used to recognize the noise statistics. The nonlinear filter, which is implemented by a hierarchical multistage system of multilayer perceptrons, outperforms state-of-the-art denoising algorithms such as those based on collaborative filtering and total variation. Compared to conventional denoising algorithms, our filter can restore images without blurring them, making it attractive for use in medical imaging where the preservation of anatomical details is critical.