Matching pursuit

Matching pursuit (MP) is a sparse approximation algorithm which involves finding the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary ${\displaystyle D}$. The basic idea is to approximately represent a signal ${\displaystyle f}$ from Hilbert space ${\displaystyle H}$ as a weighted sum of finitely many functions ${\displaystyle g_{\gamma _{n}}}$ (called atoms) taken from ${\displaystyle D}$. An approximation with ${\displaystyle N}$ atoms has the form

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