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Traditionally blind deconvolution makes the assumption that the reflectivity spike series is white. Earlier we dropped that assumption and adopted the assumption that the output spike series is sparse under a hyperbolic penalty function. This approach now here allows us to take a step further and drop the assumption of minimum phase. In this new method (what we called Bidirectional Sparse Deconvolution), We solve explicitly for the maximum phase part of the source. Results on both synthetic data and field data show clear improvements.