Prof. Nir Sharon: Method of moments for 3D single particle ab-initio modeling in Cryo-EM (19/6/19)

In single-particle cryo-electron microscopy (EM) the 3D structure of a molecule needs to be determined from its noisy 2D projection images. Each projection image is taken at an unknown viewing direction. The high level of noise makes it hard to accurately estimate the viewing directions, ultimately affecting the entire process of reconstruction. In the talk, we describe a method for obtaining a 3D ab-initio model using low order statistics without directly estimating the viewing directions. In particular, we show that the distribution of viewing directions plays a significant role, and in the case of nonuniform distribution, it allows us mathematically to estimate a model using only first two moments of the data. We discuss the advantages of our approach, together with analysis and numerical challenges that it offers.

BIO:

Nir Sharon is a Senior Lecturer at Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University. From 2015 to 2018, he has been a Post-Doctoral Research Associate with the Program of Applied and Computational Mathematics, Princeton University.
Nir earned the M.Sc. and Ph.D. degrees in applied mathematics from Tel Aviv University, Tel Aviv, and the B.A. degree in computer science from the Open University of Israel. His research interests include approximation theory, computational harmonic analysis, and scientific computing.

Amir Weiss: The Gaussian Maximum Likelihood Approach for Independent Component and Vector Analysis (26/6/19)

The Blind Source Separation (BSS) problem consists of retrieving signals of interest (termed the “sources”) from a dataset consisting of their mixtures. One of the most popular and common paradigms for solving the BSS problem is Independent Component Analysis (ICA), where the sources are assumed to be (only) mutually statistically independent random processes, and the mixtures are assumed to be linear combinations thereof, where the linear mixing operator is unknown. In this talk, we shall start with the Gaussian Maximum Likelihood (GML) approach for the semi- blind problem, in which the sources are assumed to be temporally-diverse Gaussian processes. Based on the principles of this approach, we shall present our contributions in the form of two extensions. First, we shall consider the Independent Vector Analysis (IVA) framework, which has emerged in recent years as an extension of ICA into multiple datasets of mixtures. In IVA, the sources in each dataset are independent, but may depend on sources from other datasets. We will see the benefit in using IVA, and specifically that the GML approach leads to consistent separation regardless of the sources’ true distributions. Then, the noisy Gaussian ICA problem will be addressed, in which two asymptotically optimal solutions, w.r.t. two different optimality criteria, will be presented. We shall see (both analytically and empirically) that these solutions possess attractive properties even for non-Gaussian mixtures.

BIO:

Amir Weiss received the B.Sc. (magna cum laude) and M.Sc. degrees in electrical engineering from Tel-Aviv University (TAU), Tel-Aviv, Israel, in 2013 and 2015, respectively, where he is currently pursuing his Ph.D. degree at the School of Electrical Engineering. His research and teaching areas are in statistical and digital signal processing and estimation theory. He has also been holding a researcher position in these research areas with Elbit Systems, EW and SIGINT Elisra Ltd., Holon, Israel, since 2013.
Amir has received the Nadav Levanon studies prize for graduate students, the scientific publication prize (twice) and the David Burshtein scientific publication prize all from the The Yitzhak and Chaya Weinstein Research Institute for Signal Processing in 2016, 2017, 2018 and 2019 respectively.

Yaakov Buchris: Robust and Sparse Design of Differential Microphone Arrays (12/6/19)

Design of nearly frequency-invariant (FI) broadband beamformers for several real-world applications like audio, communication, and sonar systems, is important as such beamformers can recover the signals of interest while reducing some artifacts caused during the beamforming process. Classical approaches of FI beamforming are based on constrained optimization, analytical solutions, and coherent subspace methods. Another concept is based on differential microphone arrays (DMAs), which refer to small-size superdirective arrays obtaining nearly frequencyinvariant beampatterns.
This research focuses on a sparse design of DMAs to be applied in several array geometries, like linear, planar, concentric, and more. In such arrays, the nonuniform design of the sensors’ locations enables to obtain arrays with a better robustness to array imperfections, but with a smaller number of sensors than in the uniform design. The novelty of our work relates to the fact that we are interested in broadband signals, like speech, thus, the chosen sensors should be joint to all the frequencies in the relevant bandwidth. For that purpose, we propose an incoherent joint sparse design which obtains high performance with a feasible computational complexity.

*Ph.D. Seminar under the supervision of Prof. Israel Cohen and Jacob Benesty.

BIO:

Yaakov Buchris received the B.Sc. and M.Sc. degrees in electrical engineering from the Technion-Israel Institute of Technology, Haifa, in 2005, and 2011, respectively. He is currently pursuing the Ph.D. degree in electrical engineering at the Technion-Israel Institute of Technology, Haifa, Israel.
Since 2002 he has been with RAFAEL, Advanced Defense Systems Ltd, Haifa, Israel, as a Research Engineer in the underwater acoustic communication group. Since 2005, he has also been a Teaching Assistant and a Project Supervisor with the Communications Lab and the Signal and Image Processing Lab (SIPL), Electrical Engineering Department, Technion. His research interests are statistical signal processing, adaptive filtering, digital communications, and array processing.

Tal Feld: Nonlinear spectral analysis for graph partitioning (29/5/19)

In various fields of science and engineering one seeks to solve perceptual grouping problems. Such problems can often be formulated as finding the optimal partition of a graph, where vertices represent points in feature space and edge-weights represent similarity of pairs of points. The usual objective in such partitioning is the minimization of a balanced cut, which represents low inter-cluster similarity while maintaining a reasonable size of each of the parts. Computing the optimal balanced partitioning is usually NP-hard, however, it can be approximated to the minimization of a ratio of two functionals. In this work we examine the problem of minimizing generalized Rayleigh quotients of two one-homogeneous functionals. We present an iterative algorithm which is fully analyzed and prove convergence of the iterative scheme. We use our method to estimate the optimal Cheeger cut and show experimentally that our algorithm obtains high quality classification.

Modeling of the Genome Compartments – secondary research
Chromosome conformation capture techniques are a set of molecular biology methods used to analyze the spatial organization of chromatin in a cell. Hi-C quantifies interactions between all possible pairs of fragments simultaneously, which has highlighted the critical role of spatial organization and compartmentalization on gene expression and structural variation. Deep sequencing of Hi- interaction produces a pattern known as “Checkerboard” matrix that is characterize by two different genomic compartments that overlap with several bio-track. Two regions of the same type tend to interact at higher frequency than regions of different type. We present a mechanistic probability model that overcomes many difficulties of current methods and works well on very high resolutions and low-quality data. Thus, we can now start searching for more rare biological events that could not be discover previously.

*M.Sc. Seminar under the supervision of Prof. Guy Gilboa and Prof. Noam Kaplan.

BIO:

Tal Feld received the B.Sc. degree Mathematics and Physics from the Technion – Israel Institute of Technology, Haifa, Israel, in 2016. Currently, he pursues his M.Sc. degree in Electrical Engineering from the Technion under the co-supervision of Guy Gilboa from the Electrical Engineering department and Noam Kaplan from the Medicine department.

Eyal Nitzan: Estimation Theory with Side Information for Periodic and Constrained Problems (22/5/19)

In many practical parameter estimation problems some side information regarding the unknown parameters is available. Types of side information that are commonly encountered in signal processing applications include periodicity, parametric equality and inequality constraints, and sparsity. In this research, we address some fundamental topics in estimation theory in the presence of side information. We exploit the side information by choosing proper cost functions, deriving optimal estimation methods, and developing corresponding performance bounds. In the first stage of this work we have investigated the problem of Bayesian parameter estimation in the presence of periodic side information. In periodic parameter estimation, the commonly used mean-squared-error (MSE) risk is inappropriate, since it does not take into account the periodic nature of the problem. We proposed a new class of Bayesian lower bounds on the mean-cyclic-error. This class can be interpreted as the cyclic-equivalent of the Weiss-Weinstein class of MSE lower bounds. This class was extended to provide Bayesian lower bounds for stochastic filtering with periodic side information. In the second stage of this work, we considered non-Bayesian parameter estimation under differentiable equality constraints. For this type of estimation problem, we defined proper unbiasedness in the Lehmann sense and developed new performance bounds that were shown to be more appropriate than the well-known constrained Cramér-Rao bound. In the third stage of this work, we proposed a method for optimal biased estimation. This method is based on combining Lehmann-unbiasedness under a weighted MSE risk and a penalized likelihood approach. It was shown that this method can be useful for parameter estimation under inequality constraints and can lead to estimators that uniformly outperform the minimum variance unbiased estimator and the maximum likelihood estimator.

BIO:

Eyal Nitzan received the B.Sc. and M.Sc. degrees in Electrical and Computer Engineering from the Ben-Gurion University of the Negev, Beer-Sheva, Israel, in 2012 and 2014, respectively. He is currently working toward the Ph.D. degree in the Dept. of Electrical and Computer engineering at the Ben-Gurion University of the Negev. His research interests include estimation and detection theory, statistical signal processing, and circular statistics.