Sparsity Exploitation of Mixing Matrix and Reflectivity sequence for ICA-Blind Seismic Deconvolution

This paper provides a new statistical approach to blind recovery of both earth signal and source wavelet given only the seismic traces using independent component analysis (ICA) by explicitly exploiting the sparsity of both the reflectivity sequence and the mixing matrix. Our proposed algorithm consists of three steps. Firstly, a transformation method that maps the seismic trace convolution model into multiple inputs multiple output (MIMO) instantaneous ICA model using zero padding matrices has been proposed. As a result the nonzero elements of the sparse mixing matrix contain the source wavelet. Secondly, whitening the observed seismic trace by incorporating the zero padding matrixes is conducted as a pre-processing step to exploit the sparsity of the mixing matrix. Finally, a novel logistic function that matches the sparsity of reflectivity sequence distribution has been proposed and fitted into the information maximization algorithm to obtain the demixing matrix. Experimental simulations have been accomplished to verify the proposed algorithm performance over conventional ICA algorithms. The mean square error (MSE) of estimated wavelet and estimated reflectivity sequence shows the improvement of proposed algorithm.