Accelerating Matching Pursuit for Multiple Time-Frequency Dictionaries
Matching pursuit (MP) algorithms are widely used greedy methods to find K-sparse signal approximations in redundant dictionaries. We present an acceleration technique and an implementation
of the matching pursuit algorithm acting on a multi-Gabor dictionary, i.e., a concatenation of several Gabor-type time-frequency
dictionaries, consisting of translations and modulations of possibly different windows, time- and frequency-shift parameters. The
proposed acceleration is based on pre-computing and thresholding
inner products between atoms and on updating the residual directly
in the coefficient domain, i.e., without the round-trip to the signal domain. Previously, coefficient-domain residual updates have
been dismissed as having prohibitive memory requirements. By
introducing an approximate update step, we can overcome this restriction and greatly improve the performance of matching pursuit
at a modest cost in terms of approximation quality per selected
atom. An implementation in C with Matlab and GNU Octave interfaces is available, outperforming the standard Matching Pursuit
Toolkit (MPTK) by a factor of 3.5 to 70 in the tested conditions.
Additionally, we provide experimental results illustrating the convergence of the implementation.