A Characterization of Proximity Operators

• Published in: Journal of mathematical imaging and vision Vol. 62; no. 6-7; pp. 773 - 789
• Main Authors: Gribonval, Rémi, Nikolova, Mila
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2020; Springer Nature B.V; Springer Verlag
• Subjects: Applications of Mathematics; Classical Analysis and ODEs; Computer Science; Empirical analysis; Fines & penalties; Functional Analysis; Image Processing and Computer Vision; Mathematical Methods in Physics; Mathematics; Operators (mathematics); Optimization; Proximity; Shrinkage; Signal and Image Processing; Signal,Image and Speech Processing; Group sparsity; Subdifferential; Proximity operator; Social sparsity; Convex regularization; Shrinkage operator; Nonconvex regularization; Subdiffer- ential

We characterize proximity operators, that is to say functions that map a vector to a solution of a penalized least-squares optimization problem. Proximity operators of convex penalties have been widely studied and fully characterized by Moreau. They are also widely used in practice with nonconvex pe...