A robust method for random noise suppression based on the Radon transform

Linear Radon transform, or slant-stack transform, can be used to obtain an optimally sparse representation of linear seismic events. The linear Radon transform uses a linear kernel function, and can stack the seismic data along several linear trajectories corresponding to specific slopes. The Radon transform can be formulated as a linear operator and the transform coefficients can be inverted via an iterative preconditioned least-squares method. The useful seismic signals are transformed as the sparse coefficients in the transform domain while the random noise are spreading across the transform domain or are not fitted via the Radon operator. It is advantageous to use a L2-norm data misfit to suppress the random noise but ineffective for high-amplitude erratic noise. Here, we propose a robust method to suppress both random and erratic noise based on the linear Radon transform. We iteratively transform the Huber-norm data-misfit regularization into a L2-norm regularization, which is convenient to solve using the preconditioned least-squares method. Both synthetic and field data examples are used to demonstrate the effectiveness of the proposed robust algorithm.