1. A system for distinguishing between a plurality of acoustic sources generating sound in the form of unconstrained acoustic signals captured therefrom, comprising: a transformation unit applying a spectrographic transformation upon each time-captured segment of unconstrained acoustic signal generated by one of a plurality of distinct acoustic sources, said transformation unit generating a spectral vector for each said segment; a sparse decomposition unit coupled to said transformation unit, said sparse decomposition unit selectively executing in at least a training system mode a simultaneous sparse approximation upon a joint corpus of spectral vectors for a plurality of unconstrained acoustic signal segments from at least a subset of the distinct acoustic sources, at least one of said spectral vectors generated by the spectrographic transformation, said sparse decomposition unit generating at least one sparse decomposition defined in a multi-dimensional space for each said spectral vector in terms of a representative set of decomposition atoms; a discriminant reduction unit coupled to said sparse decomposition unit, said discriminant reduction unit being executable during the training system mode to down-select from said representative set of decomposition atoms an optimal combination of atoms for cooperatively distinguishing acoustic signals emitted by different ones of the distinct acoustic sources; and, a classification unit coupled to said sparse decomposition unit, said classification unit being executable in a classification system mode to: project a spectral vector of an input acoustic signal segment onto said multi-dimensional space to generate a sparse decomposition therefor as a coefficient weighted sum of said representative set of decomposition atoms, discover for said sparse decomposition of an input acoustic signal segment a degree of similarity relative to each of the distinct acoustic sources, and determine one of the distinct acoustic sources to have generated the input acoustic signal segment as sound, according to the degree of similarity.