Compressed Sensing Based Sparse Pseudoorthogonal Radon Transform

Radon transform (RT) has been widely used in seismic data processing. The non-orthogonality of discrete Radon transform operator often leads to strong aliasing and low resolution of Radon spectrum. Much attentions are paid to inverting a sparser Radon spectrum while less work on its amplitude preserving of the inverse Radon transform (IRT). In fact, conventional IRT implies a constant-amplitude assumption. To address this problem, we propose a sparse pseudo-orthogonal Radon transform (SPO-RT) method. First we define a waveform-preserving IRT procedure by introducing a traveltime prediction error (TPE) and a spatial-variant amplitude (SVA) function to IRT. Then, we reformulate the inversion of SRT spectrum as a compressed sensing (CS) problem, and present a new matching pursuit (MP) algorithm to solve the sparse inversion problem. The proposed method may have potential prospects in many fields. In this paper, it is applied to the separation of seismic phases and inversion of ray-parameters. Synthetic data tests demonstrate the effectiveness of the proposed method.