Edge Detection, Spatial Smoothing, and Image Reconstruction With Partially Observed Multivariate Data

Situations with incomplete multivariate spatial data on a lattice are considered. The goal is to impute the missing data in the presence of edges or boundaries and recover the image. Two methods based on Bayesian hierarchical models that iterate between edge detection and spatial smoothing to impute the missing data within identified homogeneous regions are examined. Their performance is compared with another method that imputes the missing values using edge-preserving spatial smoothers with locally varying weights. The performances of the three methods are compared on artificial and real datasets. It is seen that information from the multivariate data is critical in recovering the images. An application with color images where only one of three primary colors (red, green, or blue) is observed at each pixel is used to illustrate the results.