In this paper, we introduce an algorithm for bidirectional
deconvolution that estimates the two filters simultaneously. We test the new
method on three data examples. The results show that the wavelet can
be compressed almost into a spike. When we are dealing with the zero-phase wavelet, we obtain two identical filters, a major improvement
compared with the previous bidirectional method. Another important
advantage is the low computational cost and fast convergence rate due
to the reduced number of linear iterations. However, we are surprise to see that our results are not as spiky as the ones produced by Zhang and Claerbout (2010). One possible reason may be the nature of the non-linear problem. Perhaps we need a good initial guess or preconditioning to achieve acceptable results.