A neural network solver for basis pursuit and its applications to time-frequency analysis of biomedical signals

In this paper, the authors present a new neural network model, which is called constrained smallest l(1)-norm neural network (CSl(1)NN), to implement the Basis Pursuit (BP) [1] [2] [3]. As the new and generalised one of the communities of overcomplete signal representations, the BP is considered as a large-scale linear programming problem. In contrast with the Simplex-BP or Inferior-BP in [2], the proposed CSl(1)NN-BP does not double the optimizing scale and can be implemented in real time through hardware. Taking non-stationary artificial signals and Electrogastrograms (EGGs) to test, our simulations show that the CSl(1)NN-BP 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 CSII NN-BP will be very promising for on-line time-frequency analysis of various kinds of non-stationary signals including medical data, such as EGG, EEG, and EGG, etc., with high qualify.