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There is a growing interest in deep model-based architectures (DMBAs) forsolving imaging inverse problems by combining physical measurement models andlearned image priors specified using convolutional neural nets (CNNs). Forexample, well-known frameworks for systematically designing DMBAs includeplug-and-play priors (PnP), deep unfolding (DU), and deep equilibrium models(DEQ). While the empirical performance and theoretical properties of DMBAs havebeen widely investigated, the existing work in the area has primarily focusedon their performance when the desired image prior is known exactly. This workaddresses the gap in the prior work by providing new theoretical and numericalinsights into DMBAs under mismatched CNN priors. Mismatched priors arisenaturally when there is a distribution shift between training and testing data,for example, due to test images being from a different distribution than imagesused for training the CNN prior. They also arise when the CNN prior used forinference is an approximation of some desired statistical estimator (MAP orMMSE). Our theoretical analysis provides explicit error bounds on the solutiondue to the mismatched CNN priors under a set of clearly specified assumptions.Our numerical results compare the empirical performance of DMBAs underrealistic distribution shifts and approximate statistical estimators.

Deep Model-Based Architectures for Inverse Problems under Mismatched Priors