Rank‐reduction‐based trace interpolation

Abstract

In previous papers we described a family of multidimensional filters to suppress random noise based on matrix‐rank reduction of constant‐frequency slices. Here we extend these filters to perform multidimensional trace interpolation. This requires rank reduction when some, perhaps most, of the matrix elements are unknown, a procedure called matrix completion or matrix imputation. We show how this new interpolator improves the spatial resolution of 3D data when applied prior to prestack migration. We also discuss how such interpolators might drive acquisition design.