arXiv subjects

Shirin Shoushtari

Publications and source records attributed to Shirin Shoushtari.

21 records · Page 2Linked to original sources

arXiv2022

Robustness of Deep Equilibrium Architectures to Changes in the Measurement Model

Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that have received significant attention. The key difference between the two is that the image prior in DEQ is trained by using a specific measurement model, while that in PnP is trained as a general image denoiser. This difference is behind a common assumption that PnP is more robust to changes in the measurement models compared to DEQ. This paper investigates the robustness of DEQ priors to changes in the measurement models. Our results on two imaging inverse problems suggest that DEQ priors trained under mismatched measurement models outperform image denoisers.

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arXiv2022

Deep Model-Based Architectures for Inverse Problems under Mismatched Priors

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.

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arXiv2022

Online Deep Equilibrium Learning for Regularization by Denoising

Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While traditional PnP/RED formulations have focused on priors specified using image denoisers, there is a growing interest in learning PnP/RED priors that are end-to-end optimal. The recent Deep Equilibrium Models (DEQ) framework has enabled memory-efficient end-to-end learning of PnP/RED priors by implicitly differentiating through the fixed-point equations without storing intermediate activation values. However, the dependence of the computational/memory complexity of the measurement models in PnP/RED on the total number of measurements leaves DEQ impractical for many imaging applications. We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights into its convergence and ability to approximate the traditional DEQ approach. Our numerical results suggest the potential improvements in training/testing complexity due to ODER on three distinct imaging applications.

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