Deep Model-Based Architectures for Inverse Problems under Mismatched Priors
This addresses a critical gap in applying DMBAs to real-world scenarios where prior knowledge is imperfect, though it is incremental as it builds on existing frameworks like PnP and DU.
The paper tackles the performance of deep model-based architectures (DMBAs) for imaging inverse problems when the learned CNN priors are mismatched, such as due to distribution shifts or approximations, by providing theoretical error bounds and numerical comparisons under these conditions.
There is a growing interest in deep model-based architectures (DMBAs) for solving imaging inverse problems by combining physical measurement models and learned image priors specified using convolutional neural nets (CNNs). For example, well-known frameworks for systematically designing DMBAs include plug-and-play priors (PnP), deep unfolding (DU), and deep equilibrium models (DEQ). While the empirical performance and theoretical properties of DMBAs have been widely investigated, the existing work in the area has primarily focused on their performance when the desired image prior is known exactly. This work addresses the gap in the prior work by providing new theoretical and numerical insights into DMBAs under mismatched CNN priors. Mismatched priors arise naturally when there is a distribution shift between training and testing data, for example, due to test images being from a different distribution than images used for training the CNN prior. They also arise when the CNN prior used for inference is an approximation of some desired statistical estimator (MAP or MMSE). Our theoretical analysis provides explicit error bounds on the solution due to the mismatched CNN priors under a set of clearly specified assumptions. Our numerical results compare the empirical performance of DMBAs under realistic distribution shifts and approximate statistical estimators.