Proximal Comixture Minimization Models for Image Recovery and Data Analysis
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911467859607552 |
|---|---|
| author | Combettes, Patrick L. Cornejo, Diego J. |
| author_facet | Combettes, Patrick L. Cornejo, Diego J. |
| contents | In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution arising from the \emph{a priori} knowledge and the observed data. We propose an alternative minimization model based on proximal comixtures, an operation which combines functions and linear operators in such a way that the proximity operator of the resulting function is computable explicitly in terms of the individual proximity and linear operators. The mathematical properties of this operation are analyzed and comparisons between proximal comixtures and standard composite averages are made. Numerical illustrations of the benefits of minimization models based on proximal comixtures are provided in the context of image recovery and machine learning applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proximal Comixture Minimization Models for Image Recovery and Data Analysis Combettes, Patrick L. Cornejo, Diego J. Optimization and Control In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution arising from the \emph{a priori} knowledge and the observed data. We propose an alternative minimization model based on proximal comixtures, an operation which combines functions and linear operators in such a way that the proximity operator of the resulting function is computable explicitly in terms of the individual proximity and linear operators. The mathematical properties of this operation are analyzed and comparisons between proximal comixtures and standard composite averages are made. Numerical illustrations of the benefits of minimization models based on proximal comixtures are provided in the context of image recovery and machine learning applications. |
| title | Proximal Comixture Minimization Models for Image Recovery and Data Analysis |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.09610 |