In this paper, we propose a rapid and high-accuracy Gaussian noise removal method by applying the learning linear filter used in RAISR for super-resolution. Our algorithm is a rapid local method, yet produces comparable results to the accuracy of the non-local method known for its high accuracy. The novelty of this paper is that the same processing as super-resolution is incorporated into denoising. The conventional local processing includes smoothing processing, and has a problem that high-frequency components of an original signal are lost while reducing the noise. In order to solve the problem, this method incorporates a super-resolution method that compensates for high-frequency components as post-processing. The super-resolution method utilizes a process that applies a learning linear filter according to the feature of patches in RAISR. Because the proposed method consists of local precessing, its operation is rapid compared to non local processing like BM3D.