Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion
We present a principled way of deriving a continuous relaxation of a given discontinuous shrinkage operator, which is based on two fundamental results, proximal inclusion and conversion. Using our results, the discontinuous operator is converted, via double inversion, to a continuous operator; more...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
|
| Series: | IEEE Open Journal of Signal Processing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/11034740/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We present a principled way of deriving a continuous relaxation of a given discontinuous shrinkage operator, which is based on two fundamental results, proximal inclusion and conversion. Using our results, the discontinuous operator is converted, via double inversion, to a continuous operator; more precisely, the associated “set-valued” operator is converted to a “single-valued” Lipschitz continuous operator. The first illustrative example is the firm shrinkage operator which can be derived as a continuous relaxation of the hard shrinkage operator. We also derive a new operator as a continuous relaxation of the discontinuous shrinkage operator associated with the so-called reverse ordered weighted <inline-formula><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> (ROWL) penalty. Numerical examples demonstrate potential advantages of the continuous relaxation. |
|---|---|
| ISSN: | 2644-1322 |