In this paper, we describe and study a mathematical framework for cryo-elecron microscopy. The main result, is a a proof of the admissability (correctness) and the numerical stability of the...
Singer, Amit, Shkolnisky, Yoel
The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles $\theta_1,...,\theta_n$ from $m$ noisy measurements of their...
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory (2009)
Singer, Amit, Cucuringu, Mihai
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in...
DIFFUSION INTERPRETATION OF NON-LOCAL NEIGHBORHOOD FILTERS FOR SIGNAL DENOISING (2008)
Amit Singer, Yoel Shkolnisky, Boaz Nadler
Abstract. Non-local neighborhood filters are modern and powerful techniques for image and signal denoising. In this paper, we give a probabilistic interpretation and analysis of the method. We show...
Fast Random Projections using Lean Walsh Transforms (2008)
Edo Liberty, Nir Ailon, Amit Singer
We present a k × d random projection matrix that is applicable to vectors x ∈ R d in O(d) operations if d ≥ k 2+δ′. Here, k is the minimal Johnson Lindenstrauss dimension and δ ′ is...
Graph Laplacian Tomography from Unknown Random Projections (2008)
Ronald R. Coifman, Yoel Shkolnisky, Fred J. Sigworth, Amit Singer
Abstract—We introduce a graph Laplacian based algorithm for the tomography reconstruction of a planar object from its projections taken at random unknown directions. The algorithm is shown to...
Giant Components in Biased Graph Processes (2005)
Amir, Gideon, Gurel-Gurevich, Ori, Lubetzky, Eyal, Singer, Amit
A random graph process, $\Gorg[1](n)$, is a sequence of graphs on $n$ vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution...
Boaz Nadler, Zeev Schuss, Amit Singer, Robert S. Eisenberg
Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active...
A remark on global positioning from local distances
Finding the global positioning of points in Euclidean space from a local or partial set of pairwise distances is a problem in geometry that emerges naturally in sensor networks and NMR spectroscopy...