Yonina Eldar

Emmanuel J. Candes, Yonina Eldar, Thomas Strohmer et al.

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.

Amit Aflalo, Shai Bagon, Tamar Kashti et al.

Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Current approaches often rely on extracting deep features from pre-trained networks to construct a graph, and classical clustering methods like k-means and normalized-cuts are then applied as a post-processing step. However, this approach reduces the high-dimensional information encoded in the features to pair-wise scalar affinities. To address this limitation, this study introduces a lightweight Graph Neural Network (GNN) to replace classical clustering methods while optimizing for the same clustering objective function. Unlike existing methods, our GNN takes both the pair-wise affinities between local image features and the raw features as input. This direct connection between the raw features and the clustering objective enables us to implicitly perform classification of the clusters between different graphs, resulting in part semantic segmentation without the need for additional post-processing steps. We demonstrate how classical clustering objectives can be formulated as self-supervised loss functions for training an image segmentation GNN. Furthermore, we employ the Correlation-Clustering (CC) objective to perform clustering without defining the number of clusters, allowing for k-less clustering. We apply the proposed method for object localization, segmentation, and semantic part segmentation tasks, surpassing state-of-the-art performance on multiple benchmarks.

Alon Gonen, Dan Rosenbaum, Yonina Eldar et al.

The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity