Alternating Direction Method of Multipliers for Negative Binomial Model with The Weighted Difference of Anisotropic and Isotropic Total Variation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917761934950400 |
|---|---|
| author | Lu, Yu Bui, Kevin Marcia, Roummel F. |
| author_facet | Lu, Yu Bui, Kevin Marcia, Roummel F. |
| contents | In many applications such as medical imaging, the measurement data represent counts of photons hitting a detector. Such counts in low-photon settings are often modeled using a Poisson distribution. However, this model assumes that the mean and variance of the signal's noise distribution are equal. For overdispersed data where the variance is greater than the mean, the negative binomial distribution is a more appropriate statistical model. In this paper, we propose an optimization approach for recovering images corrupted by overdispersed Poisson noise. In particular, we incorporate a weighted anisotropic-isotropic total variation regularizer, which avoids staircasing artifacts that are introduced by a regular total variation penalty. We use an alternating direction method of multipliers, where each subproblem has a closed-form solution. Numerical experiments demonstrate the effectiveness of our proposed approach, especially in very photon-limited settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alternating Direction Method of Multipliers for Negative Binomial Model with The Weighted Difference of Anisotropic and Isotropic Total Variation Lu, Yu Bui, Kevin Marcia, Roummel F. Image and Video Processing Computer Vision and Pattern Recognition Optimization and Control In many applications such as medical imaging, the measurement data represent counts of photons hitting a detector. Such counts in low-photon settings are often modeled using a Poisson distribution. However, this model assumes that the mean and variance of the signal's noise distribution are equal. For overdispersed data where the variance is greater than the mean, the negative binomial distribution is a more appropriate statistical model. In this paper, we propose an optimization approach for recovering images corrupted by overdispersed Poisson noise. In particular, we incorporate a weighted anisotropic-isotropic total variation regularizer, which avoids staircasing artifacts that are introduced by a regular total variation penalty. We use an alternating direction method of multipliers, where each subproblem has a closed-form solution. Numerical experiments demonstrate the effectiveness of our proposed approach, especially in very photon-limited settings. |
| title | Alternating Direction Method of Multipliers for Negative Binomial Model with The Weighted Difference of Anisotropic and Isotropic Total Variation |
| topic | Image and Video Processing Computer Vision and Pattern Recognition Optimization and Control |
| url | https://arxiv.org/abs/2408.16117 |