~~Speaker: Anatoly Khina
Ph.D. student under the supervision of Prof. Uri Erez

Wednesday, July 8th, 2015 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering

Simultaneous Matrix Decompositions for Gaussian Communication Networks

Abstract
A central concept in matrix analysis is the decomposition of a matrix into a product of orthogonal (or unitary) matrices and a diagonal/triangular one, e.g., unitary diagonalization of a symmetric matrix, and more generally the singular-value decomposition, and the QR decomposition. Such decompositions are of particular importance for multi-antenna point-to-point physical-layer communications, where the channel gains are represented by a (channel) matrix. Transforming the channel matrix into diagonal/triangular forms, in this case, allows to reduce the coding task to that of coding for scalar (single-antenna) channels. Thus, the modulation and coding tasks are effectively decoupled and the performance is dictated by the diagonal values. In this work we develop new joint matrix decompositions of several matrices using the same unitary matrix on one side (corresponding to a joint transmitter or receiver) to achieve desired properties for the resulting diagonals. An important special case is a transformation leading to equal diagonals for all matrices simultaneously. This, in turn, allows to construct practical schemes for various communications settings, as well as deriving new theoretic bounds for others.

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Gal Malach, 
M.Sc. student under the supervision of Prof. Nahum Kiryati and Prof. Nir Sochen

Wednesday, June 24th, 2015 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering

Unsupervised methods for joint segmentation of an image set

Abstract

Segmentation of a region of interest in an image is significantly influenced by the availability of prior information. However, in many cases such prior information is not available or not compatible with the image in hand. Luckily, nowadays applications can benefit from the large availability of images with similar or close contents, e.g., multiple overlapping viewpoints of the same object or use of various image acquisition methods. As a result, there is a shift from the classical prior based segmentation to a co-segmentation approach. Under the co-segmentation framework simultaneous segmentation of two images is applied where each segmentation is supported by the other to utilize the large commonality between the two images. In the first part of this work we review the current state-of-the-art co-segmentation methods and present a generalization of the pair-wise methods to account for image ensemble. Furthermore, we set a theoretical framework to draw the connection between our generalized pair-wise co-segmentation method to a probabilistic atlas-based approach.

In the second part of this work, we present a novel method for co-segmentation of common regions of interest (ROIs) in multiple image volumes of possibly different qualities or in the presence of inconsistencies. In contrast to the classical atlas-based approaches, only a single annotated image is used as a prior. The joint segmentation process is supported by the evolving segmentation of each of the individual images while accounting for the varying confidence levels. The proposed approach uses soft segmentation. Labeling uncertainty of a given voxel is determined by its spatial proximity to the estimated ROI's boundaries and the dynamically changing segmentation's confidence, learned throughout the joint segmentation process. Our contribution consists of a robust segmentation method that advances existing co-segmentation algorithms. The proposed algorithm is supported by a theoretical derivation which shows that it is a generalization of previous approaches. Promising results are demonstrated for the joint segmentation of neuroanatomical structures across 50 MR scans of different subjects. The proposed algorithm supports multi-modal data where each modality reveals different features of the ROI. A significant variance in the confidence levels was observed when using the proposed method for cross-modality joint segmentation of brain tumor tissues (BraTS).

~~Speaker:  Or Ordentlich
PhD student under the supervision of Prof. Uri Erez

Monday, June 29th, 2015  at  15:00
Room 011, Kitot Bldg., Faculty of Engineering

Integer-Forcing for Multiterminal Communication Problems

Abstract

    Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output (MIMO) or multiple-access (MAC) channel. Integer-forcing is applicable when all transmitters use nested linear/lattice codes.

    Building on the IF framework, we derive new theoretical results and develop new low-complexity coding schemes for several problems.

   We begin by studying the capacity region of the Gaussian MAC under the constraint that all users transmit from a chain of nested lattice codes. Interestingly, the obtained rate-region depends on number-theoretic properties of the channel gains. Then, we apply these results in conjunction with lattice interference alignment to approximate the sum capacity of the symmetric K-user Gaussian interference channel.

    We next apply the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under an MSE distortion measure. The performance of the proposed scheme closely follows Berger-Tung's inner bound.  Moreover, a one-shot version of IF source coding is described and analyzed.