Cooperative Greedy Pursuit algorithms
are designed for producing the atomic decomposition of
a signal partition, subjected to a global constraint
The cooperation between partition units is realized in
i)By ranking the partition units for
their sequential stepwise approximation:
Hierarchiezed Blockwise Orthogonal Matching Pursuit
(HBW-OMP) and Hierarchiezed Blockwise Optimized Orthogonal Matching Pursuit (HBW-OOMP)
ii)By ranking the partition units for stepwise downgrading
of the whole approximation:
Hierarchiezed Blockwise Backwards
Optimized Orthogonal Matching Pursuit (HBW-BOOMP).
iii)By allowing for migration of atoms, from some partition
units to another partition units, to improve the
Hierarchiezed Blockwise Swapping Refinement
of OMP/OOMP (HBW-SR-OMP/OOMP).
The algorithm details are given in the paper:
The MATLAB routines for implementing the numerical
examples in the papers are available in the archive Cooperative.zip.
A description of the archive content can be found in the file Cooperative_info.pdf.
The routines are dedicated to the use of
trigonometric dictionaries for achieving high quality
approximation of musical signals. The examples illustrate:
i)The gain in the sparsity achieved by
redundant trigonometric dictionaries, in comparison with
the corresponding trigonometric orthogonal basis
(133% improvement in the piano melody given below,
approximated up to SNR=36dB).
ii)The gain in the sparsity achieved by the proposed
strategies, restricted by a global constraint on sparsity,
in comparison with the standard OMP/OOMP approximation
of every partition to the same quality (133% improvement in the piano melody
Piano melody. Credit: Julius O. Smith,
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University, website
Play original melody
Piano melody approximated up to SNR=36dB
Play sparse approximation