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

arXiv: https://arxiv.org/abs/2402.15635 · HTML: https://mlsanity.com/paper/2402.15635/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 53 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [SUNet: Swin Transformer UNet for Image Denoising](https://mlsanity.com/paper/2202.14009/) (2022)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [Blind Image Deblurring with Unknown Kernel Size and Substantial Noise](https://mlsanity.com/paper/2208.09483/) (2022)
- [Practical Phase Retrieval Using Double Deep Image Priors](https://mlsanity.com/paper/2211.00799/) (2022)
- [One-dimensional Deep Image Prior for Time Series Inverse Problems](https://mlsanity.com/paper/1904.08594/) (2019)
- [Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework](https://mlsanity.com/paper/1708.01142/) (2017)
- [Convergence Rate Improvement of Richardson and Newton-Schulz Iterations](https://mlsanity.com/paper/2008.11480/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multilook Coherent Imaging: Theoretical Guarantees and Algorithms](https://mlsanity.com/paper/2505.23594/) (2025)
- [Maximum Likelihood Reconstruction for Multi-Look Digital Holography with Markov-Modeled Speckle Correlation](https://mlsanity.com/paper/2604.20154/) (2026)
- [Untrained Neural Nets for Snapshot Compressive Imaging: Theory and Algorithms](https://mlsanity.com/paper/2406.03694/) (2024)
- [Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle](https://mlsanity.com/paper/2602.10344/) (2026)

## Abstract (arXiv)

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.