A local radon transform for seismic random noise attenuation

The Radon transform can sparsify the seismic data assuming that the events follow a certain type of trajectories. Commonly known Radon transforms include linear, parabolic, and hyperbolic transforms, which are usually exploited to process pre-stack data with the parabolic and hyperbolic kernels, or structurally simple post-stack seismic data with distinct linear events. We develop a new Radon transform by introducing a local sparsification strategy into the traditional method. We first select a set of spatial positions, where the local Radon transform is centered in, then we construct the Radon transform with a fixed width; the linear-kernel is shared by all local Radon transforms. The local Radon coefficients are obtained directly from solving an augmented Radon transform model. To enforce the sparsity of coefficients, we apply an L1-norm regularization to the inverse model and solve it via a preconditioned least-squares method. We use a seismic shot gather with curved events and a complicated post-stack field dataset to demonstrate the superiority of the proposed method in dealing with complicated seismic data compared with the conventional Radon transform.