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The aim of sparse approximation is to estimate a sparse signal according tothe measurement matrix and an observation vector. It is widely used in dataanalytics, image processing, and communication, etc. Up to now, a lot ofresearch has been done in this area, and many off-the-shelf algorithms havebeen proposed. However, most of them cannot offer a real-time solution. To someextent, this shortcoming limits its application prospects. To address thisissue, we devise a novel sparse approximation algorithm based on Lagrangeprogramming neural network (LPNN), locally competitive algorithm (LCA), andprojection theorem. LPNN and LCA are both analog neural network which can helpus get a real-time solution. The non-differentiable objective function can besolved by the concept of LCA. Utilizing the projection theorem, we furthermodify the dynamics and proposed a new system with global asymptotic stability.Simulation results show that the proposed sparse approximation method has thereal-time solutions with satisfactory MSEs.

Fast L1-Minimization Algorithm for Sparse Approximation Based on an Improved LPNN-LCA framework