  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 approximation, 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 advantage of
the strategy is illustrated 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.

Data Structures and Algorithms