A Multiple-point Geostatistics Method for filling gaps in Landsat ETM plus SLC-off images

The Scan Line Corrector (SLC), which compensates for the forward motion of Landsat 7, failed on May 31, 2003. The lack of SLC resulted in data gaps in the observed images, affecting the spatially continuous fields that were usually provided. Fortunately, the observations acquired by Landsat 7 are highly geometrically and radiometrically accurate compared with many other sensors, allowing the opportunity to develop gap-filling approaches to address the problem. How best to do this remains an open question. A variety of simple and effective methods based on different ideas have been proposed. Most of these can be classified into two categories: deterministic interpolation or geostatistical estimation. Deterministic interpolation approaches calculate the values of the unknown pixels based on an assumed continuity with the values of neighbouring data points. Geostatistical approaches formulate a spatial model of variability that is used to estimate the missing values as well as to quantify the uncertainty of these missing values. Most current approaches are only applicable for relatively homogeneous areas. For example they cannot satisfactorily predict the presence of narrow or small objects such as roads or streams. As a result, such objects can be truncated after interpolation. This problem may drastically constrain the application of filled SLC-off images. In this study, a multiple-point geostatistics approach, the Direct Sampling method, is adopted as a solution to fill Landsat 7 images. The Direct Sampling method uses a conditional stochastic resampling of known areas in the observation image to simulate the unknown locations. This approach can reuse the complex patterns present in the incomplete image, and has the capacity to simulate narrow or small objects. Moreover, being a geostatistical method, it allows for the generation of multiple interpolations to compute uncertainty bounds on the interpolated values. Here, the Direct Sampling method is applied to both univariate and multivariate cases to demonstrate its application. Numerical experiments indicate that the Direct Sampling method is able to fill the gaps satisfactory, especially when combining the target image with a temporally close image. The results are satisfactory for filling narrow objects like roads or streams. Compared with other gap filling method, the Direct Sampling method is relatively simple and easily employed. However, it also has limitations, such as the appropriate selection of parameters, which can greatly influence the simulation effect and computation time. Further research advancing the optimisation and providing guidance on parameter selection is required.