An interactive system for separating image information from noise information in noisy input images may include a structure-preserving filter capable of separating high- and low-frequency image structures from random noise. The system may access data representing an initially denoised image and a corresponding initial noise layer, apply the structure-preserving filter to the noise layer to extract image structure, and combine the extracted structure with the initially denoised image to produce a refined image, restoring structure incorrectly removed from an image by a previous denoising operation. The system may provide brush tools to identify regions on which to apply the filter and mechanisms to specify filter parameter values. The filter may be applied iteratively to improve results, and may be employed in noise-consistent image editing tasks to preserve original image noise. The filter may be implemented by program instructions stored on a computer readable medium and executable by CPUs and/or GPUs.