  We describe a new algorithm to solve a particular phase retrieval problem,
that has wide applications in audio processing: the reconstruction of a
function from its scalogram, that is from the modulus of its wavelet transform.
It is a multiscale iterative algorithm. To efficiently propagate phase
information from low to high frequencies, it uses an equivalent formulation of
the phase retrieval problem that involves the holomorphic extension of the
wavelet transform. Our numerical results, on audio and non-audio signals, show
that reconstruction is precise and stable to noise. The algorithm has a linear
complexity in the size of the signal, up to logarithmic factors, and can thus
be used on large signals.
