Other families of noise

I tried the same processing with exponential and gaussian noise. Unfortunately, the L¹ minimization is no more efficient. The noise samples now have various amplitudes, about the same repartitions as the original trace, and cannot be isolated from the seismic samples by the original criterion of small weight: they have all kinds of weighting. The L¹ norm itself does not improve the result of the L² deconvolution; the most usual way to suppress the noise is to use large damping factors, which is not a typical characteristic of the L¹ norm. Moreover, even if the noise n is gaussian, white, and uncorrelated with the seismic data, the L¹ normal equations cannot use these properties, because the correlations terms (n^Tn, y^Tn) will be weighted by the matrix W, and replaced by n^TWn and y^TWn (which may not vanish). I will suggest in the last part a method to cope simultaneously with two kinds of noise, for example gaussian and spiky noise, using L¹ and L² norms simultaneously.