Systems and methods of denoising images are described. In one aspect, spatially-shifted forward transforms of the input image are computed. Each forward transform is computed based on a denoiser transform Z having an associated transpose Z', wherein a matrix multiplication between Z and Z' produces a diagonal matrix .LAMBDA., Z=F(D), F specifies a mapping from coefficients of D to coefficients of Z, and D substantially corresponds to a frequency-domain transform. The forward transforms are denoised based on nonlinear mappings derived from quantization values linked to the input image. Spatially-shifted inverse transforms of the denoised forward transforms are computed. Each inverse transform is computed based on Z and Z'. An output image is computed based on a combination of spatially-shifted inverse transforms.