Matching pursuit is a type of numerical technique which involves finding the "best matching" projections of multidimensional data onto an over-complete dictionary . The basic idea is to represent a signal from Hilbert space as a weighted sum of functions (called atoms) taken from :
where indexes the atoms that have been chosen, and a weighting factor (an amplitude) for each atom. Given a fixed dictionary, matching pursuit will first find the one atom that has the biggest inner product with the signal, then subtract the contribution due to that atom, and repeat the process until the signal is satisfactorily decomposed.
For comparison, consider the Fourier series representation of a signal - this can be described in the terms given above, where the dictionary is built from sinusoidal basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals . By taking an extremely redundant dictionary we can look in it for functions that best match a signal . Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression.
Read more about Matching Pursuit: The Algorithm, Properties, Applications, Extensions
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