A neural network solver for Basis Pursuit

In this paper, the authors present a new neural network model, which can be called constrained smallest l₁-norm neural network (CSl₁NN), to implement the Basis Pursuit (BP)^[1-3]. As the new and generalised one of the communities of over-complete signal representations, the BP is considered as a larger-scale linear programming problem. In contrast with the Simplex-BP or interior-BP in [2], the proposed CSl₁NN-BP does not double the optimizing scale and can be implemented in real time through hardware. Taking non-static nary artificial signals to test, our simulations show that the CSl₁NN presents an excellent convergence performance for a wide range of time-frequency (TF) dictionaries and has a higher joint TF resolution not only than the traditional Wigner Distribution (WD), but also than recently rising other overcomplete representation methods, such as Method of Frames (MOF)^[9], Best Orthogonal Basis (BOB)^[10] and Matching Pursuit (MP)^[4]. Combining the high resolution with the fast implementation, the CSl₁ NN-BP will be very promising for on-line time-frequency analysis of various kinds of non-stationary signals with high quality.