Most iterative optimization algorithms for motion, depth estimation or scene reconstruction, both sparse and dense, rely on a coarse and reliable dense initialization to bootstrap their optimization procedure. This makes techniques important that allow to obtain a dense but still approximative representation of a desired 2D structure (e.g., depth maps, optical flow, disparity maps) from a very sparse measurement of this structure. The method presented here exploits the complete information given by the principal component analysis (PCA), the principal basis and its prior distribution. The method is able to determine a dense reconstruction even if only a very sparse measurement is available. When facing such situations, typically the number of principal components is further reduced which results in a loss of expressiveness of the basis. We overcome this problem and inject prior knowledge in a maximum a posteriori (MAP) approach. We test our approach on the KITTI and the Virtual KITTI dataset and focus on the interpolation of depth maps for driving scenes. The evaluation of the results shows good agreement to the ground truth and is clearly superior to the results of an interpolation by the nearest neighbor method which disregards statistical information.