Application of barrier algorithm in signal reconstruction via compressive sampling

In this work signal reconstruction via compressive sampling is investigated. Compressive sampling theory extends the classical Shannon-Nyquist sampling theory for signals with arbitrary support. Conditions for exact signal reconstruction are covered. Signal reconstruction via compressive sampling is shown to be an ℓ1-norm minimization problem which can be solved as a norm approximation problem. Norm approximation problem is cast as a linear program and barrier method is implemented in its solution. Numerical experiments are conducted to compare the empirical bounds obtained via the barrier algorithm against the analytical results.