Gradient projection for linearly constrained convex optimization in sparse signal recovery

The ℓ₂-ℓ₁ compressed sensing minimization problem can be solved efficiently by gradient projection. In imaging applications, the signal of interest corresponds to nonnegative pixel intensities; thus, with additional nonnegativity constraints on the reconstruction, the resulting constrained minimization problem becomes more challenging to solve. In this paper, we propose a gradient projection approach for sparse signal recovery where the reconstruction is subject to nonnegativity constraints. Numerical results are presented to demonstrate the effectiveness of this approach.