Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Image restoration tasks are ill-posed problems, typically solved with priors. Since the optimal prior is the exact unknown density of natural images, actual priors are only approximate and typically restricted to small patches. This raises several questions: How much may  hope to improve current restoration results with future sophisticated algorithms? And more fundamentally, even with perfect knowledge of natural image statistics, what is the inherent ambiguity of the problem? In addition, since most current methods are limited to finite support patches or kernels, what is the relation beten the patch complexity of natural images, patch size, and restoration errors? Focusing on image denoising,  make several contributions. First, in light of computational constraints,  study the relation beten denoising gain and sample size requirements in a non parametric approach.  present a law of diminishing return, namely that with increasing patch size, rare patches not only require a much larger dataset, but also gain little from it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second,  study absolute denoising limits, regardless of the algorithm used, and the converge rate to them as a function of patch size. Scale invariance of natural images plays a key role here and implies both a strictly positive lor bound on denoising and a por law convergence. Extrapolating this parametric law gives a ballpark estimate of the best achievable denoising, suggesting that some improvement, although modest, is still possible.
['Anat Levin', 'Boaz Nadler', 'Frédo Durand', 'William T. Freeman']
I am writing a research paper on a idea Patch complexity, finite pixel correlations and optimal denoising
[{"from": "human", "value": "I am writing a research paper on a idea Patch complexity, finite pixel correlations and optimal denoising"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Image restoration tasks are ill-posed problems, typically solved with priors. Since the optimal prior is the exact unknown density of natural images, actual priors are only approximate and typically restricted to small patches. This raises several questions: How much may  hope to improve current restoration results with future sophisticated algorithms? And more fundamentally, even with perfect knowledge of natural image statistics, what is the inherent ambiguity of the problem? In addition, since most current methods are limited to finite support patches or kernels, what is the relation beten the patch complexity of natural images, patch size, and restoration errors? Focusing on image denoising,  make several contributions. First, in light of computational constraints,  study the relation beten denoising gain and sample size requirements in a non parametric approach.  present a law of diminishing return, namely that with increasing patch size, rare patches not only require a much larger dataset, but also gain little from it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second,  study absolute denoising limits, regardless of the algorithm used, and the converge rate to them as a function of patch size. Scale invariance of natural images plays a key role here and implies both a strictly positive lor bound on denoising and a por law convergence. Extrapolating this parametric law gives a ballpark estimate of the best achievable denoising, suggesting that some improvement, although modest, is still possible."}]