Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition

subjected to a global constraint on sparsity. The approach aims at producing a high quality

sparse approximation of the whole signal, using highly coherent redundant dictionaries. The

cooperation takes place by ranking the partition units for their sequential stepwise approxima-

tion, and is realized by means of i)forward steps for the upgrading of an approximation and/or

ii) backward steps for the corresponding downgrading. The advantages of the strategy is illus-

trated by producing high quality approximations of music signals using redundant trigonometric

dictionaries. In addition to rendering stunning improvements in sparsity with respect to the

concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach

via the Fast Fourier Transform.