This paper aimed to formulate image noise reduction as an optimization problem and denoise the target image using matrix low rank approximation. Considering the fact that the smaller pieces of an image are more similar (more dependent) in natural images; therefore, it is more logical to use low rank approximation on smaller pieces of the image. In the proposed method, the image corrupted with AWGN (Additive White Gaussian Noise) is locally denoised, and the optimization problem of low rank approximation is solved on all fixed-size patches (Windows with pixels needing to be processed). For practical purposes, this method can be implemented parallelly, because it can simultaneously handle different image patches. This is one of the advantages of this method. In all noise reduction methods, the two factors, namely the amount of the noise removed from the image and the preservation of the edges (vital details), are very important. In the proposed method, all the new ideas-including the use of TI image (Training Image) and SVD adaptive basis, iterability of the algorithm and patch labeling-have all been proved efficient in producing sharper images, and good edge preservation. They also had an acceptable speed compared to the state-of-the-art denoising methods.