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This paper presents a new paradigm for signal decomposition and reconstruction that is based on the selection of a sparse set of basis functions. Based on recently reported results, we note that this framework is equivalent to approximating the signal using Support Vector Machines. Two different algorithms of modeling sensory activity within the barrel cortex of a rat are presented. First, a slightly modified approach to the Independent Component Analysis (ICA) algorithm and its application to the investigation of Evoked Potentials (EP), and second, an Evolutionary Algorithm (EA) for learning an overcomplete basis of the EP components by viewing it as probabilistic model of the observed data. The results of the experiments conducted using these two approaches as well as a discussion concerning a possible utilization of those results are also provided.