  We construct an estimator of the L\'evy density of a pure jump L\'evy
process, possibly of infinite variation, from the discrete observation of one
trajectory at high frequency. The novelty of our procedure is that we directly
estimate the L\'evy density relying on a pathwise strategy, whereas existing
procedures rely on spectral techniques. By taking advantage of a compound
Poisson approximation, we circumvent the use of spectral techniques and in
particular of the L\'evy--Khintchine formula. A linear wavelet estimator is
built and its performance is studied in terms of $L_p$ loss functions, $p\geq
1$, over Besov balls. We recover classical nonparametric rates for finite
variation L\'evy processes and for a large nonparametric class of symmetric
infinite variation L\'evy processes. We show that the procedure is robust when
the estimation set gets close to the critical value 0 and also discuss its
robustness to the presence of a Brownian part.
