Bagged Deep Image Prior for Recovering Images in the Presence of Speckle
  Noise
Xi Chen Zhewen Hou Christopher A. Metzler Arian Maleki Shirin Jalali
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.