In this work, we consider an additive white Gaussian noise (AWGN) model on the image patches in the context of patch-based image denoising. From this, we propose a derivation of the induced models on the centered patch of noise and on the DC component of the noise. These models allow us to treat separately the two component. We provides experiments with the HDMI method [1] that lead to denoising quality improvements, particularly for residual low frequency noise.