arXiv subjects

Jon Tamir

Publications and source records attributed to Jon Tamir.

4 recordsLinked to original sources

arXiv2026

Analyzing Model Misspecification in Quantitative MRI: Application to Perfusion ASL

Quantitative MRI (qMRI) involves parameter estimation governed by an explicit signal model. However, these models are often confounded and difficult to validate in vivo. A model is misspecified when the assumed signal model differs from the true data-generating process. Under misspecification, the variance of any unbiased estimator is lower-bounded by the misspecified Cramer-Rao bound (MCRB), and maximum-likelihood estimates (MLE) may exhibit bias and inconsistency. Based on these principles, we assess misspecification in qMRI using two tests: (i) examining whether empirical MCRB asymptotically approaches the CRB as repeated measurements increase; (ii) comparing MLE estimates from two equal-sized subsets and evaluating whether their empirical variance aligns with theoretical CRB predictions. We demonstrate the framework using arterial spin labeling (ASL) as an illustrative example. Our result shows the commonly used ASL signal model appears to be specified in the brain and moderately misspecified in the kidney. The proposed framework offers a general, theoretically grounded approach for assessing model validity in quantitative MRI.

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arXiv2025

Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements

Diffusion models (DMs) have rapidly emerged as a powerful framework for image generation and restoration. However, existing DMs are primarily trained in a supervised manner by using a large corpus of clean images. This reliance on clean data poses fundamental challenges in many real-world scenarios, where acquiring noise-free data is hard or infeasible, and only noisy and potentially incomplete measurements are available. While some methods can train DMs using noisy data, they are generally effective only when the amount of noise is very mild or when some additional noise-free data is available. In addition, existing methods for training DMs from incomplete measurements require access to multiple complementary acquisition processes, an assumption that poses a significant practical limitation. Here we introduce the first approach for learning DMs for image restoration using only noisy measurement data from a single operator. As a first key contribution, we show that DMs, and more broadly minimum mean squared error denoisers, exhibit a weak form of scale equivariance linking rescaling in signal amplitude to changes in noise intensity. We then leverage this theoretical insight to develop a denoising score-matching strategy that generalizes robustly to noise levels lower than those present in the training data, thereby enabling the learning of DMs from noisy measurements. To further address the challenges of incomplete and noisy data, we integrate our method with equivariant imaging, a complementary self-supervised learning framework that exploits the inherent invariants of imaging problems, to train DMs for image restoration from single-operator measurements that are both incomplete and noisy. We validate the effectiveness of our approach through extensive experiments on image denoising, demosaicing, and inpainting, along with comparisons with the state of the art.

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arXiv2020

Memory-efficient Learning for Large-scale Computational Imaging -- NeurIPS deep inverse workshop

Computational imaging systems jointly design computation and hardware to retrieve information which is not traditionally accessible with standard imaging systems. Recently, critical aspects such as experimental design and image priors are optimized through deep neural networks formed by the unrolled iterations of classical physics-based reconstructions (termed physics-based networks). However, for real-world large-scale systems, computing gradients via backpropagation restricts learning due to memory limitations of graphical processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable data-driven design for large-scale computational imaging. We demonstrate our methods practicality on two large-scale systems: super-resolution optical microscopy and multi-channel magnetic resonance imaging.

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arXiv2020

Memory-efficient Learning for Large-scale Computational Imaging

Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical model-based reconstructions (termed physics-based networks). However, for real-world large-scale inverse problems, computing gradients via backpropagation is infeasible due to memory limitations of graphics processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable data-driven design for large-scale computational imaging systems. We demonstrate our method on a small-scale compressed sensing example, as well as two large-scale real-world systems: multi-channel magnetic resonance imaging and super-resolution optical microscopy.

cs.CV↗