Technical perspective: Images everywhere looking for models
Deriving appropriate regularization terms, priors or models, has occupied the research community since the early days of digital image processing. Different image models can be appropriate for different types of images; for example, MRI and natural images should have different models. The basic underlying concept is that local image information repeats itself across the non-local image. Noise, on the other hand, is expected in numerous scenarios to be random. Therefore, collecting those similar local regions all across the image, the noise can be eliminated by simple estimators based on having multiple observations of the same underlying signal under different noise conditions. The self-similarity model assumes the dictionary is the image itself, or actually its local patches. All these models indicate that images, and in particular image patches, do not actually live in the ambient high-dimensional space, but in some much lower dimensional stratification embedded on it.
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