274 research outputs found
Matrix recovery using Split Bregman
In this paper we address the problem of recovering a matrix, with inherent
low rank structure, from its lower dimensional projections. This problem is
frequently encountered in wide range of areas including pattern recognition,
wireless sensor networks, control systems, recommender systems, image/video
reconstruction etc. Both in theory and practice, the most optimal way to solve
the low rank matrix recovery problem is via nuclear norm minimization. In this
paper, we propose a Split Bregman algorithm for nuclear norm minimization. The
use of Bregman technique improves the convergence speed of our algorithm and
gives a higher success rate. Also, the accuracy of reconstruction is much
better even for cases where small number of linear measurements are available.
Our claim is supported by empirical results obtained using our algorithm and
its comparison to other existing methods for matrix recovery. The algorithms
are compared on the basis of NMSE, execution time and success rate for varying
ranks and sampling ratios
Distributed Basis Pursuit
We propose a distributed algorithm for solving the optimization problem Basis
Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear
system Ax = b and is used, for example, in compressed sensing for
reconstruction. Our algorithm solves BP on a distributed platform such as a
sensor network, and is designed to minimize the communication between nodes.
The algorithm only requires the network to be connected, has no notion of a
central processing node, and no node has access to the entire matrix A at any
time. We consider two scenarios in which either the columns or the rows of A
are distributed among the compute nodes. Our algorithm, named D-ADMM, is a
decentralized implementation of the alternating direction method of
multipliers. We show through numerical simulation that our algorithm requires
considerably less communications between the nodes than the state-of-the-art
algorithms.Comment: Preprint of the journal version of the paper; IEEE Transactions on
Signal Processing, Vol. 60, Issue 4, April, 201
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