Minimum fuel neural networks and their applications to overcomplete signalrepresentations

The overcomplete signal representation (OSR) is a recently established adap tive signal representation method. As an adaptive signal representation met hod, the OSR means that a given signal is decomposed onto a number of optim al basis components, which are found from an overcomplete basis dictionary via some optimization algorithms, such as the matching pursuit (MP), method of frame (MOF) and basis pursuit (BP), Such ideas are actually very close to or exactly-the same as solving a minimum fuel (MF) problem. The MF probl em isa well-established minimum L-1-norm optimization:model with linear con straints, The:BP-based OSR proposed by Chen and Donoho is exactly the same model as the MF model. The work of Chen and Donoho showed that the MF model could be used as a generalized method for solving an OSR problem and it-ou tperformed the MP and the MOF. In this paper, the neural implementation of the MF model and its applications to-the OSR are presented. A new neural ne twork, namely the minimum fuel neural network (MFNN), is constructed and it s convergence in solving the MF problem is proven theoretically and validat ed experimentally. Compared with the implementation of the original BP, the MFNN does not double the scales of the problem and its convergence is inde pendent of initial conditions. It is shown that the MFNN is promising for t he application in the OSR's of-various kinds of nonstationary signals with a high time-frequency resolution,and feasibility of real-time implementatio n. As an extension, a two-dimensional (2-D) MF model suitable for image dat a compression is also proposed and its neural implementation is presented.