A neural network for ℓ1−ℓ2 minimization based on scaled gradient projection: Application to compressed sensing

Since compressed sensing was introduced in 2006, ℓ1−ℓ2 minimization admits a large number of applications in signal processing, statistical inference, magnetic resonance imaging (MRI), computed tomography (CT), etc. In this paper, we present a neural network for ℓ1−ℓ2 minimization based on scaled gradient projection. We prove that it is stable in the sense of Lyapunov and converges to an optimal solution of the ℓ1−ℓ2 minimization. We show that the proposed neural network is feasible and efficient for compressed sensing via simulation examples.