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Instead, we follow a<jats:italic>local self-similarity<\/jats:italic>assumption on natural images and extract patches from extremely localized regions in the input image. This allows us to reduce considerably the nearest-patch search time without compromising quality in most images. Tests, that we perform and report, show that the local self-similarity assumption holds better for small scaling factors where there are more example patches of greater relevance. We implement these small scalings using dedicated novel nondyadic filter banks, that we derive based on principles that model the upscaling process. Moreover, the new filters are nearly biorthogonal and hence produce high-resolution images that are highly consistent with the input image without solving implicit back-projection equations. The local and explicit nature of our algorithm makes it simple, efficient, and allows a trivial parallel implementation on a GPU. 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