Image noise filters usually assume noise as white Gaussian. However, in a capturing pipeline, noise often becomes spatially correlated due to in-camera processing that aims to suppress the noise and increase the compression rate. Mostly, only high-frequency noise components are suppressed since the image signal is more likely to appear in the low-frequency components of the captured image. As a result, noise emerges as coarse grain which makes white (all-pass) noise filters ineffective, especially when the resolution of the target display is lower than the captured image. Denoising of image approximation in coarse scale has the advantage of removing low-frequency noise, however, lack of spatial resolution degrades the image quality. This paper presents an approach for a coarse-grain removal. Our approach utilizes existing white Gaussian noise filters to address low-frequency component of spatially correlated noises, employing pixel decoupling, local shrinkage, and soft thresholding. Subjective and objective results show that the proposed approach better handles low-frequency noise compared to related work.