Extensions
A popular extension of Matching Pursuit (MP) is its orthogonal version: Orthogonal Matching Pursuit (OMP). The main difference from MP is that after every step, all the coefficients extracted so far are updated, by computing the orthogonal projection of the signal onto the set of atoms selected so far. This can lead to better results than standard MP, but requires more computation.
In fact, this algorithm approximates the sparse problem :
with the pseudo-norm (i.e. the number of nonzero elements of ).
Extensions such as Multichannel MP and Multichannel OMP allow to process multicomponents signals.
Matching pursuit is related to the field of compressed sensing and has been extended by researchers in that community. Notable extensions are Orthogonal Matching Pursuit (OMP), Stagewise OMP (StOMP), and compressive sampling matching pursuit (CoSaMP).
Read more about this topic: Matching Pursuit
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