Sound recordings include transients and sustained parts. Their analysis with a basis expansion is not rich enough to represent efficiently all such components. Pursuit algorithms choose the decomposition vectors depending upon the signal properties. The dictionary among which these vectors are selected is much larger than a basis. Matching Pursuit is fast to compute, but can provide coarse representations. Basis Pursuit gives a better representation but is very expensive in terms of calculation time. This paper develops a High Resolution Matching Pursuit : it is a fast, high time-resolution, time-frequency anal;ysis algorithm, that makes it likely to be used for musical applications.