Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise

Xi Chen, Zhewen Hou, Christopher Metzler, Arian Maleki, Shirin Jalali
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:6803-6832, 2024.

Abstract

We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-chen24q, title = {Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise}, author = {Chen, Xi and Hou, Zhewen and Metzler, Christopher and Maleki, Arian and Jalali, Shirin}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {6803--6832}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/chen24q/chen24q.pdf}, url = {https://proceedings.mlr.press/v235/chen24q.html}, abstract = {We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.} }
Endnote
%0 Conference Paper %T Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise %A Xi Chen %A Zhewen Hou %A Christopher Metzler %A Arian Maleki %A Shirin Jalali %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-chen24q %I PMLR %P 6803--6832 %U https://proceedings.mlr.press/v235/chen24q.html %V 235 %X We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.
APA
Chen, X., Hou, Z., Metzler, C., Maleki, A. & Jalali, S.. (2024). Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:6803-6832 Available from https://proceedings.mlr.press/v235/chen24q.html.

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