Unrolled Generative Compound Gaussian Network for Computer Tomography

As many inverse problems arising in synthetic apertures and computer tomography are ill-posed, prior information about the solution space is incorporated to establish regularity on the solutions of inverse problems. Often, this prior information is a practitioner chosen statistical distribution or structure of the desired inverse problem solution. Recently, the generative network from a generative adversarial network (GAN) has been implemented as a learned prior information in imaging inverse problems. In this paper, we construct a novel deep neural network (DNN), by applying algorithm unrolling to an alternating direction method of multipliers implementation, that is fundamentally informed by a dual-structured prior combining a learned GAN prior with the encompassing compound Gaussian class of statistical distributions. Through empirical analysis of our novel DNN in tomographic imaging, we demonstrate a significant improvement in reconstructed image quality over prior art methods that use a learned GAN prior.