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Sparse signal approximation can be used to design efficient low bit-rate coding schemes. It heavily relies on the ability to design appropriate dictionaries and corresponding decomposition algorithms. The size of the dictionary, and therefore its resolution, is a key parameter that handles the tradeoff between sparsity and tractability. This work proposes the use of a non adaptive random sequence of subdictionaries in a greedy decomposition process, thus browsing a larger dictionary space in a probabilistic fashion with no additional projection cost nor parameter estimation. This technique leads to very sparse decompositions, at a controlled computational complexity. Experimental evaluation is provided as proof of concept for low bit rate compression of audio signals.