Sparse inversion of the Radon coefficients in the presence of erratic noise with application to simultaneous seismic source processing

In recent years, efforts have been made in designing simultaneous-source strategies that permit to save seismic acquisition costs. Seismic sources are fired with time overlap producing seismic records that contain a mixture of sources. These records need to be unmixed before seismic imaging. The unmixing process can be written as an inverse problem where one attempts to solve a linear system of equations to estimate the unmixed seismic data. This article describes a source separation process where we assume that source interferences can be modelled via an erratic noise process. In addition, the ideal unmixed data are assumed to be sparse in the Hyperbolic Radon transform domain. Therefore, the source separation problem is posed as an inverse problem where one seeks to retrieve a sparse model from observations contaminated with erratic (sparse) noise. We present a modification of the fast iterative shrinkage-thresholding algorithm that permits to cope with the simultaneous estimation of sparse Radon coefficients that are required to synthesize the unmixed data. The algorithm is also utilized to estimate the erratic noise caused by source interferences.