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

We give and prove two new and fundamental properties of total variation minimizing function regularization (TV Regularization): 1) edge locations of function (e.g. image) features tend to be preserved, and under certain conditions, are preserved exactly ; 2) intensity change experienced by individual features is inversely proportional to the scale of each feature. More generally, we describe both qualitatively and quantitatively the exact eects of TV Regularization in R 1 , R 2 and R 3 . We give and prove exact analytic solutions to the nonlinear TV Regularization problem for simple but important cases, which can be used to better understand the eects of TV Regularization for more general cases. The formulae we give describe the eect of TV Regularization when applied to noise-contaminated radially symmetric image features. These formulae also accurately predict the eects of TV Regularization when it is applied to more general functions. Our results help explain how and why TV...