A joint matrix minimization approach for seismic wavefield recovery

Reconstruction of the seismic wavefield from sub-sampled data is important and necessary in seismic image processing; this is partly due to limitations of the observations which usually yield incomplete data. To make the best of the observed seismic signals, we propose a joint matrix minimization model to recover the seismic wavefield. Employing matrix instead of vector as weight variable can express all the sub-sampled traces simultaneously. This scheme utilizes the collective representation rather than an individual one to recover a given set of sub-samples. The matrix model takes the interrelation of the multiple observations into account to facilitate recovery, for example, the similarity of the same seismic trace and distinctions of different ones. Hence an l(2, p)(0 < p ≤ 1)-regularized joint matrix minimization is formulated which has some computational challenges especially when p is in (0, 1). For solving the involved matrix optimization problem, a unified algorithm is developed and the convergence analysis is accordingly demonstrated for a range of parameters. Numerical experiments on synthetic and field data examples exhibit the efficient performance of the joint technique. Both reconstruction accuracy and computational cost indicate that the new strategy achieves good performance in seismic wavefield recovery and has potential for practical applications.