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Elias Nehme

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Uncertainty Quantification via Neural Posterior Principal Components

Sep 27, 2023
Elias Nehme, Omer Yair, Tomer Michaeli

Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel estimates. However, a heatmap of per-pixel variances is typically of little practical use, as it does not capture the strong correlations between pixels. A more natural measure of uncertainty corresponds to the variances along the principal components (PCs) of the posterior distribution. Theoretically, the PCs can be computed by applying PCA on samples generated from a conditional generative model for the input image. However, this requires generating a very large number of samples at test time, which is painfully slow with the current state-of-the-art (diffusion) models. In this work, we present a method for predicting the PCs of the posterior distribution for any input image, in a single forward pass of a neural network. Our method can either wrap around a pre-trained model that was trained to minimize the mean square error (MSE), or can be trained from scratch to output both a predicted image and the posterior PCs. We showcase our method on multiple inverse problems in imaging, including denoising, inpainting, super-resolution, and biological image-to-image translation. Our method reliably conveys instance-adaptive uncertainty directions, achieving uncertainty quantification comparable with posterior samplers while being orders of magnitude faster. Examples are available at

* Accepted to NeurIPS 2023, webpage at 
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Roadmap on Deep Learning for Microscopy

Mar 07, 2023
Giovanni Volpe, Carolina Wählby, Lei Tian, Michael Hecht, Artur Yakimovich, Kristina Monakhova, Laura Waller, Ivo F. Sbalzarini, Christopher A. Metzler, Mingyang Xie, Kevin Zhang, Isaac C. D. Lenton, Halina Rubinsztein-Dunlop, Daniel Brunner, Bijie Bai, Aydogan Ozcan, Daniel Midtvedt, Hao Wang, Nataša Sladoje, Joakim Lindblad, Jason T. Smith, Marien Ochoa, Margarida Barroso, Xavier Intes, Tong Qiu, Li-Yu Yu, Sixian You, Yongtao Liu, Maxim A. Ziatdinov, Sergei V. Kalinin, Arlo Sheridan, Uri Manor, Elias Nehme, Ofri Goldenberg, Yoav Shechtman, Henrik K. Moberg, Christoph Langhammer, Barbora Špačková, Saga Helgadottir, Benjamin Midtvedt, Aykut Argun, Tobias Thalheim, Frank Cichos, Stefano Bo, Lars Hubatsch, Jesus Pineda, Carlo Manzo, Harshith Bachimanchi, Erik Selander, Antoni Homs-Corbera, Martin Fränzl, Kevin de Haan, Yair Rivenson, Zofia Korczak, Caroline Beck Adiels, Mite Mijalkov, Dániel Veréb, Yu-Wei Chang, Joana B. Pereira, Damian Matuszewski, Gustaf Kylberg, Ida-Maria Sintorn, Juan C. Caicedo, Beth A Cimini, Muyinatu A. Lediju Bell, Bruno M. Saraiva, Guillaume Jacquemet, Ricardo Henriques, Wei Ouyang, Trang Le, Estibaliz Gómez-de-Mariscal, Daniel Sage, Arrate Muñoz-Barrutia, Ebba Josefson Lindqvist, Johanna Bergman

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Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

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Learning an optimal PSF-pair for ultra-dense 3D localization microscopy

Sep 29, 2020
Elias Nehme, Boris Ferdman, Lucien E. Weiss, Tal Naor, Daniel Freedman, Tomer Michaeli, Yoav Shechtman

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A long-standing challenge in multiple-particle-tracking is the accurate and precise 3D localization of individual particles at close proximity. One established approach for snapshot 3D imaging is point-spread-function (PSF) engineering, in which the PSF is modified to encode the axial information. However, engineered PSFs are challenging to localize at high densities due to lateral PSF overlaps. Here we suggest using multiple PSFs simultaneously to help overcome this challenge, and investigate the problem of engineering multiple PSFs for dense 3D localization. We implement our approach using a bifurcated optical system that modifies two separate PSFs, and design the PSFs using three different approaches including end-to-end learning. We demonstrate our approach experimentally by volumetric imaging of fluorescently labelled telomeres in cells.

* 20 pages, 20 figures 
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