Dantzig selector homotopy with dynamic measurements

The Dantzig selector is a near ideal estimator for recovery of sparse signals from linear measurements in the presence of noise. It is a convex optimization problem which can be recast into a linear program (LP) for real data, and solved using some LP solver. In this paper we present an alternative approach to solve the Dantzig selector which we call "Primal Dual pursuit" or "PD pursuit". It is a homotopy continuation based algorithm, which iteratively computes the solution of Dantzig selector for a series of relaxed problems. At each step the previous solution is updated using the optimality conditions defined by the Dantzig selector. We will also discuss an extension of PD pursuit which can quickly update the solution for Dantzig selector when new measurements are added to the system. We will present the derivation and working details of these algorithms.