A fast-convergence POCS seismic denoising and reconstruction method

Abstract

The effi ciency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defi nes the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coeffi cient section and slower than in the exponential threshold in the small-coeffi cient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak refl ections. To improve the fl exibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and fi eld data. The results suggest that the inversely proportional threshold model improves the computational effi ciency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.

A POCS super resolution restoration algorithm based on BM3D

“…The super resolution restoration using POCS is convenient to bring into prior knowledge and build complex image degradation model, which is a more mature method widely used in many occasions 5 , 6 . However, this method is sensitive to noise and the restoration quality will decline dramatically for image sequence with low SNR 7 , 8 . Considering the good denoising performance and the capability of preserving edge details, we consider combining BM3D and POCS, in which the image sequence with high SNR are obtained from the low resolution image sequence using BM3D filtering 9 – 11 .…”