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

TL;DR

This paper presents a theoretical analysis and a novel algorithmic approach using bagged Deep Image Priors for improved image recovery in speckle noise, achieving state-of-the-art results.

Contribution

It provides the first theoretical upper bound on MSE for deep image prior-based estimators and introduces Bagged-DIP with efficient matrix inverse computation.

Findings

Theoretical MSE bound depends on model parameters and noise characteristics.

Bagged-DIP with Newton-Schulz method outperforms existing algorithms.

Achieves state-of-the-art image recovery performance in speckle noise scenarios.

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.