Department of Mathematics
On L1 data fitting and concave regularization for image recovery
We propose a new family of cost functions for signal and image recovery: they are composed of ℓ1 data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks. © 2013 Society for Industrial and Applied Mathematics.
ℓ1 data fitting, Continuation methods, Image recovery, Inverse problems, MRI, Multidimensional shrinkage, Nonsmooth and nonconvex analysis, Nonsmooth and nonconvex minimization, Penalty methods, Properties of minimizers, Regularization, Total variation, Variable-splitting, Variational methods
Source Publication Title
SIAM Journal on Scientific Computing
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Nikolova, Mila, Michael K. Ng, and Chi-Pan Tam. "On L1 data fitting and concave regularization for image recovery." SIAM Journal on Scientific Computing 35.1 (2013): A397-A430.