Inversion of traveltime data using ray tracing is a bad posed problem. High frequency approximation is a reason of the bad conditioning, meanwhile employing fat rays in the inversion process mitigates the severity of the problem. Decomposed levels in wavelet domain could provide a desired representation of rays so that in a scale-wise inversion in wavelet domain, initially long wavelengths of model is estimated and gradually details is added to the model. If estimation of high order coefficients be ignored, the method is equivalent to a smoothing regularization method. Velocity model has a sparse representation in wavelet domain so the estimated coefficients should preserve this specification too. FISTA is used for solving the problem and the method have applied on synthetic and real data and results are compared with other methods.