The paper is devoted to the task of estimation of the parameters of spatially correlated noise and noise suppression in images. Several schemes of noise removal, including multiscale ones, are considered. A convolutional neural network (CNN) for blind estimation of the spectrum of spatially correlated noise images is proposed. It is shown that the proposed network in combination with the BM3D filter provides more efficient noise suppression than existing solutions. A CNN for prediction of the denoising parameters for DRUNet denoiser is also proposed and analyzed. It is shown that the usage of this network and DRUNet for multiscale denoising in comparison with other methods provides better quality of image denoising and processing speed for a wide range of sizes of “noise grain”.