Edward T. Reehorst

Edward T. Reehorst, Philip Schniter

In out-of-distribution (OOD) detection, one is asked to classify whether a test sample comes from a known inlier distribution or not. We focus on the case where the inlier distribution is defined by a training dataset and there exists no additional knowledge about the novelties that one is likely to encounter. This problem is also referred to as novelty detection, one-class classification, and unsupervised anomaly detection. The current literature suggests that contrastive learning techniques are state-of-the-art for OOD detection. We aim to improve on those techniques by combining/ensembling their scores using the framework of null hypothesis testing and, in particular, a novel generalized likelihood ratio test (GLRT). We demonstrate that our proposed GLRT-based technique outperforms the state-of-the-art CSI and SupCSI techniques from Tack et al. 2020 in dataset-vs-dataset experiments with CIFAR-10, SVHN, LSUN, ImageNet, and CIFAR-100, as well as leave-one-class-out experiments with CIFAR-10. We also demonstrate that our GLRT outperforms the score-combining methods of Fisher, Bonferroni, Simes, Benjamini-Hochwald, and Stouffer in our application.

Rizwan Ahmad, Charles A. Bouman, Gregery T. Buzzard et al.

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

Edward T. Reehorst, Philip Schniter

Regularization by Denoising (RED), as recently proposed by Romano, Elad, and Milanfar, is powerful image-recovery framework that aims to minimize an explicit regularization objective constructed from a plug-in image-denoising function. Experimental evidence suggests that the RED algorithms are state-of-the-art. We claim, however, that explicit regularization does not explain the RED algorithms. In particular, we show that many of the expressions in the paper by Romano et al. hold only when the denoiser has a symmetric Jacobian, and we demonstrate that such symmetry does not occur with practical denoisers such as non-local means, BM3D, TNRD, and DnCNN. To explain the RED algorithms, we propose a new framework called Score-Matching by Denoising (SMD), which aims to match a "score" (i.e., the gradient of a log-prior). We then show tight connections between SMD, kernel density estimation, and constrained minimum mean-squared error denoising. Furthermore, we interpret the RED algorithms from Romano et al. and propose new algorithms with acceleration and convergence guarantees. Finally, we show that the RED algorithms seek a consensus equilibrium solution, which facilitates a comparison to plug-and-play ADMM.