Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise
This work addresses image recovery in the presence of speckle noise, which is incremental as it builds upon deep image prior methods with theoretical and algorithmic enhancements.
The paper tackles the problem of recovering complex-valued signals from measurements corrupted by speckle noise by establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis and introducing Bagged Deep Image Priors (Bagged-DIP) with projected gradient descent, achieving state-of-the-art performance.
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.