Blind Deconvolution with Toeplitz-structured Sparse Total Least Squares Algorithm

Blind deconvolution simultaneously solves for the reflectivity series and the wavelet given the noise corrupted seismic recordings. This is an ill-posed problem and difficult to solve. Developing a reliable single channel blind deconvolution technique is an ongoing research. Here, we formulated the blind deconvolution as a fully perturbed linear regression model and developed an efficient iterative algorithm based on Total least squares (TLS) method. Unfortunately, TLS method, with or without regularization, does not provide consistent estimators for the under-determined linear system of equations. To remedy this shortcoming, we added more constraints into the equations. We assume that the reflectivity series is sparse and moreover, to reduce the model space and the number of unknowns, the algorithm preserves the Toeplitz structure of the data matrix. In addition, there is no assumption about the phase of the wavelet. The developed algorithm is an alternating minimization method and can be used for different applications such as blind deconvolution, perturbed compressive sensing and dictionary learning. In this paper, we only focused on blind deconvolution. The performance of the algorithm is evaluated on synthetic and real datasets. Real data examples are belonging to lines A and D of the Teapot Dome seismic survey.