Comparison of the MM algorithm and least squares deconvolution method for the recognition of thin layers

Deconvolution problems involve estimating an unknown input when the signal and the response of an LTI system are known and lead to wavelet compression and increase the temporal resolution. However, in practice, the output signal is noisy. For some systems, the deconvolution problem is simple, but for the non-invertible or almost non-invertible systems, the problem is more complex. The use of the exact inverse of the systems leads to the amplification of the noise. The reflectivity sequence is the representation of the layers of the earth. The resulted compression leads to a high-resolution image of the earth. The outcomes exhibit that the reflection coefficient significantly improves after application of the MM algorithm on synthetic and real data, compared to the least squares and the frequency spectrum methods after the application of the algorithm.