Modified Sparse Multichannel Blind Deconvolution

Summary Euclid deconvolution is a multichannel algorithm that leads to the estimation of the multichannel seismic reflectivity via the solution of homogeneous system of equations. In the ideal case, the eigenvector associated to the minimum nonzero eigenvalue of the homogenous system of equations is an estimator of the multichannel reflectivity. However, small amounts of noise impinge on the identification of the eigenvector associated to the impulse response. Recently, we proposed a method called SMBD that solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the unknown multichannel impulse response. The method can accurately estimate the seismic reflectivity and wavelet in the presence of a moderate amount of noise. However, it does not model the noise properly and there is no automatic way for defining the regularization parameter. In this abstract, we tried to improve the SMBD algorithm by including an extra term to handle additive noise. Moreover, in our new algorithm the regularization parameters can be automatically estimated via line search and cross validation procedures. The method is successfully tested on a realistic synthetic example and on marine and land real datasets.