The overcomplete signal representation (OSR) is a recently established adaptive signal representation method. As an adaptive signal representation method, the OSR means that a given signal is decomposed onto a number of optimal basis components, which are found from an overcomplete basis dictionary via some optimization algorithms, such as the matching pursuit (MP), method of frame (MOE) and basis pursuit (BP). Such ideas are actually very close to or exactly the same as solving a minimum fuel (ME) problem. The ME problem is a well-established minimum L{sub}1-norm optimization model with linear constraints. The BP-based OSR proposed by Chen and Donoho is exactly the same model as the ME model. The work of Chen and Donoho showed that the ME model could be used as a generalized method for solving an OSR problem and it outperformed the MP and the MOE. In this paper, the neural implementation of the ME model and its applications to the OSR are presented. A new neural network, namely the minimum fuel neural network (MFNN), is constructed and its convergence in solving the ME problem is proven theoretically and validated experimentally. Compared with the implementation of the original BP, the MENN does not double the scales of the problem and its convergence is independent of initial conditions. It is shown that the MENN is promising for the application in the OSR's of various kinds of nonstationary signals with a high time-frequency resolution and feasibility of real-time implementation. As an extension, a two-dimensional (2-D) ME model suitable for image data compression is also proposed and its neural implementation is presented.
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