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—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least-norm solution of the underdetermined linear system 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… (More)

—We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via ℓ1-ℓ1 and ℓ1-ℓ2 minimization. We then establish bounds on the number of measurements required by… (More)

—We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via ℓ1-ℓ1 and ℓ1-ℓ2 minimization. We then provide lower bounds on the number of measurements that these problems require for… (More)

We propose a recursive algorithm for estimating time-varying signals from a few linear measurements. The signals are assumed sparse, with unknown support, and are described by a dynamical model. In each iteration, the algorithm solves an ℓ1-ℓ1 minimization problem and estimates the number of measurements that it has to take at the next iteration. These… (More)

—We propose a distributed algorithm, named D-ADMM, for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem, the cost function is the sum of all the agents' private cost functions, and the constraint set is the intersection of all the agents' private constraint sets. We require the… (More)

— Many problems in control can be modeled as an optimization problem over a network of nodes. Solving them with distributed algorithms provides advantages over centralized solutions, such as privacy and the ability to process data locally. In this paper, we solve optimization problems in networks where each node requires only partial knowledge of the… (More)

Basis Pursuit (BP) finds a minimum 1-norm vector z that satisfies the underdetermined linear system Mz = b, where the matrix M and vector b are given. Lately, BP has attracted attention because of its application in compressed sensing, where it is used to reconstruct signals by finding the sparsest solutions of linear systems. In this paper, we propose a… (More)

The Basis Pursuit (BP) problem consists in finding a least 1 norm solution of the underdetermined linear system Ax = b. It arises in many areas of electrical engineering and applied mathematics. Applications include signal compression and modeling, estimation, fitting , and compressed sensing. In this paper, we explore methods for solving the BP in a… (More)

—In this paper we consider a network with P nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector x ⋆ minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function… (More)

—We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for ℓ1-ℓ1 minimization, is recursive and computes… (More)