We propose using overlapping, tapered windows to process seismic data in parallel. This method consists of numerically tight linear operators and adjoints that are suitable for use in iterative algorithms. This method is also highly scalable and makes parallel processing of large seismic data sets feasible. We use this scheme to define the Parallel Windowed Fast Discrete Curvelet Transform (PWFDCT), which we apply to a seismic data interpolation algorithm. The successful performance of our parallel processing scheme and algorithm on a two-dimensional synthetic data is shown.