Sparse Signal Reconstruction using BasisPursuit Algorithm

Compressive Sensing acquire sparse signal significantly at very lower rate than Nyquist sampling rate. For this, a low complexity compressed sensing operation is defined and it is the combination of sampling and compression. The signals formed from compressed sensing operation are compressible signals and a set of random linear measurements accurately reconstructs compressible signals with the use of nonlinear or convex reconstruction algorithms. Basis Pursuit algorithm is one of the convex optimization algorithms to reconstruct the sparse signal. The l1 minimization theory for linear programming problems is used to formulate the compressive sensing method. Interior point method is used to solve the basis pursuit algorithm for sparse signal reconstruction. In this paper, the methodology of reconstructing sparse signal using basis pursuit algorithm is discussed.