A Lagrange Programming Neural Network Approach with an ?0-Norm Sparsity Measurement for Sparse Recovery and Its Circuit Realization

Many analog neural network approaches for sparse recovery were based on using ?1-norm as the surrogate of ?0-norm. This paper proposes an model, namely Lagrange programming with ?p objective and quadratic constraint (LPNN-LPQC), ?0-norm sparsity measurement solving constrained basis pursuit denoise (CBPDN) problem. As is non-differentiable, we first use a differentiable ?p-norm-like function to approximate However, this does not have explicit expression and, thus, locally competitive algorithm (LCA) concept handle nonexistence expression. With LCA approach, dynamics are defined by internal state vector. In proposed thresholding elements conventional in optimization. also circuit realization elements. theoretical side, prove that equilibrium points our method satisfy Karush Kuhn Tucker (KKT) conditions approximated CBPDN problem, asymptotically stable. We perform large scale simulation various algorithms models. Simulation results show better than or comparable several state-of-art numerical algorithms, it