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We present a novel method for image enhancement aimed at restoring or hallucinating fine-grained natural image details while retaining well-detailed areas intact. To that end, we employ convolutional neural network trained using aligned patches from pairs of high-and low-quality images depicting the same scenery. Our training procedure includes our novel modulated retention loss which makes the learning concentrate on image areas requiring improvement, while retaining the rest. To address the problem of large-scale consistency of fine-grained details (for example, integrity of long hair strands), we propose the use of nested convolution kernels, which allows leveraging fractal selfsimilarity of feature maps produced from the input image. Our experiments show clear improvement of subjective quality of fine-grained details (human hair, garment fabric) in image areas which suffered from detail degradation. Objective quality measurements (using non-reference image quality metrics) show competitive performance of our method compared to the state-of-the-art image enhancement methods.