# Matching pursuits with time-frequency dictionaries

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### Cites background from "Matching pursuits with time-frequen..."

...…;a NX i=1 (yi; Fm 1(xi) + h(xi; a)) (9) and then Fm(x) = Fm 1(x) + mh(x; am): (10) In signal processing this strategy is called \matching pursuit" (Mallat and Zhang 1993) where (y; F ) is squared{error loss and the fh(x; am)g M 1 are called basis functions, usually taken from an over{complete…...

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...(y; F ) = 1 2 (y F ) 2 jy F j (jy F j =2) jy F j > : (15)...

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...The solution to (15) (16) can be obtained by standard iterative methods (see Huber 1964)....

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### Cites background from "Matching pursuits with time-frequen..."

...1) How many measurements are necessary to reconstruct the signal? 2) Given these measurements, what algorithms can perform the reconstruction task? As we will see, signal recovery is dual to sparse approximation, a problem of significant interest [1]–[5]....

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...The algorithm later developed a life of its own in the signal processing [1], [17], [18] and approximation theory [25], [5] literatures....

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