Novel approach to coherent imaging in the presence of speckle noise

In coherent imaging systems like SAR and digital holography, speckle noise is effectively mitigated using the multilook or multishot approach. Utilizing maximum likelihood estimation (MLE), we recently theoretically and algorithmically showed the feasibility of effectively recovering a signal from multilook measurements, even when each look is severely under-determined. Our method leverages the "Deep Image Prior (DIP) hypothesis", which posits that images can be effectively represented within untrained neural networks with fewer parameters than the total pixel count, using i.i.d. noises as inputs. We also developed a computationally efficient algorithm inspired by projected gradient descent to solve the MLE optimization, incorporating a model bagged-DIP concept for the projection step. This paper explores the method's applicability to deblurring in coherent imaging, where the forward model involves a blurring kernel amidst speckle noise and additive noise - a significant challenge with broad applications. We introduce a novel iterative algorithm to address these issues, enabling multi-look deblurring without simplifying or approximating the MLE cost function.