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.

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.

Shai Biton: Nonlinear Eigenfunctions – The Functional’s Natural Shapes And When To Use Them (23/01/2019)

A fundamental concept in solving inverse problems is the use of regularizers, which yield more physical and less-oscillatory solutions. Total variation (TV) has been widely used as an edge-preserving regularizer. However, objects are often over-regularized by TV, becoming blob-like convex structures of low curvature. This was explained by Andreu et al. by analyzing eigenfunctions of the TV subgradient operator. A compelling approach to better preserve structures is to use anisotropic functionals, which adapt the regularization in an image-driven manner, with strong regularization along edges and low across them. Adaptive anisotropic TV (A^2TV) was successfully used in several studies in the past decade. However, until now there was no theory formulating the type of structures which can be perfectly preserved (eigenfunctions induced by A^2TV). In this study, we address this question.

BIO: Shai Biton received his B.Sc. degree from the Department of Electrical Engineering, summa cum laude, from Ort Braude, Karmiel, in 2011. Currently, he pursues his M.Sc. degree in Electrical Engineering from the Technion – Israel Institute of Technology, Haifa. His current research interests are medical imaging, thermal imaging, image reconstruction, and deep learning.

{*}M.Sc. student under the supervision of Prof. Guy Gilboa.

The lecture will take place on Wednesday, 23/01/2019

at 14:30 in room 1061 of the Andre and Bella Meyer Building.

Department of Electrical Engineering, The Technion, Haifa.

For the complete SP&S seminar schedule visit:

https://sps-seminar.net.technion.ac.il

Dr. Yaron Orenstein : Deep learning for protein-RNA interactions (5/12/2018)

Protein-RNA binding, mediated through both RNA sequence and structure, plays a vital role in many cellular processes, including neuro-degenerative diseases. Modeling the sequence and structure binding preferences of an RNA-binding protein is a key computational challenge. Accurate models will enable prediction of new interactions and a better understanding of the binding mechanism.

In this talk, I will describe a new deep learning based approach to learn RNA sequence and structure binding preferences from large biological datasets. I will present the results of our algorithm outperforming the state of the art, both in vitro and in vivo. I will give examples of the biological insights we can gain by applying our neural networks to larger datasets of protein-RNA interactions. I will conclude with open questions and a discussion on the success of deep learning in computational biology.

No biological background is assumed or required for the purpose of the talk.

Bio:

Yaron is a Senior Lecturer at the Department of Electrical and Computer Engineering, BGU. He spent his post-doctoral training at CSAIL, MIT and the Simons Institute, UC Berkeley. Previously, he received his Ph.D and M.Sc degrees from CS and EE, TAU, respectively. Yaron completed his bachelor’s degree in Computer Science and Electrical Engineering at TAU.

Oren Solomon: Fast Super-resolution Imaging in Optics and Ultrasound: From Sparsity to Deep Learning (21/11/2018)

Until recent years, the spatial resolution of diffractive imaging devices such as microscopes and ultrasound machines, was considered to be fundamentally limited, as first established by Ernst Karl Abbe almost 150 years ago. The 2014 Nobel prize in chemistry was awarded for methods which proved that although the diffraction limit poses a physical limitation, it can nonetheless be circumvented by altering the conventional measurement process in fluorescence microscopy. Drawing inspiration from microscopy, similar methods were applied to ultrasound imaging, achieving a precise mapping of sub-diffraction vascular networks deep within the tissue. However, although such techniques demonstrated unprecedented resolving power beyond the limit of diffraction, they lack in temporal resolution. Thus, the ability to image dynamic processes in sub-diffraction resolution is severely limited in these techniques.

In my work, I outline the main limitations of the pioneering super-resolution techniques, and present how fast super-resolution can be achieved by increasing fluorophore density and exploiting structural and statistical priors of the acquired signal. The first part of my work demonstrates that by exploiting sparsity in the correlation

domain, fluorescence microscopy can achieve sub-diffraction imaging with resolution comparable to state-of-the-art, while requiring two orders less the number of exposures. Next, I present how similar ideas can be extended to contrast enhanced ultrasound to achieve time-lapse imaging of super-resolved hemodynamic changes. Moreover, I also explain how in ultrasound we can further exploit the inherent motion of contrast agents to achieve Doppler processing in sub-diffraction resolution on one

hand, and on the other, how blood flow can be used as a structural prior for super-resolution. Lastly, I show that recent developments in the field of deep learning can also be applied to ultrasound imaging to achieve super-resolution, and to suppress tissue clutter signal for better visualization of blood vessels, as an initial step for further advanced processing.

BIO:

Oren Solomon is a Ph.D student under the supervision of Prof. Yonina Eldar.

Oren received his B. Sc. in electrical engineering from Ben-Gurion University , Beer-Sheva, in 2008 and his M. Sc. in electrical engineering from Tel-Aviv University in 2014. He is currently pursuing his Ph. D. degree in electrical engineering at the Technion-Israel Institute of Technology. His main research interests include theoretical aspects of signal processing, sampling theory, compressed sensing, medical imaging and optics, as well as deep learning. Oren was awarded The Andrew and Erna Finci Viterbi Fellowship Program for 2017.

Dr. Tamir Bendory: Estimation in extreme noise levels with application to cryo-electron microscopy (14/11/2018)

Single-particle cryo-electron microscopy (cryo-EM) is an innovative technology for elucidating structures of biological molecules at atomic-scale resolution. In a cryo-EM experiment, tomographic projections of a molecule, taken at unknown viewing directions, are embedded in highly noisy images at unknown locations. The cryo-EM problem is to estimate the 3-D structure of a molecule from these noisy images.

Inspired by cryo-EM, the talk will focus on two estimation problems: multi-reference alignment and blind deconvolution. These problems abstract away much of the intricacies of cryo-EM, while retaining some of its essential features. In multi-reference alignment, we aim to estimate a signal from its noisy, rotated observations. While the rotations and the signal are unknown, the goal is only to estimate the signal. In the blind deconvolution problem, the goal is to estimate a signal from its convolution with an unknown, sparse signal in the presence of noise. Focusing on the low SNR regime, I will propose the method of moments as a computationally efficient estimation framework for both problems and will introduce its properties. In particular, I will show that the method of moments allows estimating the sought signal accurately in any noise level, provided sufficiently many observations are collected, with only one pass over the data. I will then argue that the same principles carry through to cryo-EM, show examples, and draw potential implications.