Edge-preserving and scale-dependent properties of total variation regularization

摘要: We give and prove two new fundamental properties of total-variation-minimizing function regularization (TV regularization): edge locations features tend to be preserved, under certain conditions are preserved exactly; intensity change experienced by individual is inversely proportional the scale each feature. exact analytic solutions TV problem for simple but important cases. These can also used better understand effects more general Our results explain why how TV-minimizing image restoration remove noise while leaving relatively intact larger-scaled features, thus especially effective in restoring images with features. Although a global problem, our show that on often quite local. us understanding what types degradation most effectively improved schemes, they potentially lead intelligently designed schemes.