Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction

A reconstruction method known as Projection Onto Convex Sets (POCS) is an effective, uncomplicated and robust method for the recovery of irregularly missing seismic traces. However, slow convergence of the POCS reconstruction method could jeopardize its computational appeal. For this reason, we investigate the performance of the POCS reconstruction method in terms of different threshold schedules and present a new data driven threshold that leads to an efficient implementation of the POCS method. In particular, we show that high quality solutions can be obtained in a few iterations. In addition, we address an important issue with the classical implementations of POCS reconstruction in that they cannot interpolate regularly missing data. To solve this problem, we introduce a masking operator that is based on a dominant dip scanning method into the POCS iteration. At the end, we present a variant of the POCS method that permits de-noising seismic volumes during the reconstruction stage. This is achieved by defining a weighted trace re-insertion strategy that alleviates the influence of noisy traces in the final reconstruction of the seismic volume. We show the effectiveness of the proposed method using synthetic and field data.