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Sampling Beyond Limits: The Illusion of Super-Resolution
Sampling and reconstruction in signal processing adhere to the Nyquist theorem, which states that to accurately reconstruct a signal, one must sample at least twice the frequency of the signal. However, advancements in super-resolution generative models challenge this traditional principle. These models can create high-resolution images from low-resolution inputs by 'hallucinating' additional details based on learned patterns in data. While they provide impressive results, this process essentially circumvents the foundational rules of sampling and reconstruction by leveraging inherent structures in the data, illustrating a tension between theoretical principles and practical innovations in image generation.