A novel framework for spatially estimating unknown image data is presented. Common applications include inpainting, concealment of transmission errors, prediction in video coding, etc. Firstly, a segmentation of the spatial neighborhood of the area to be estimated is performed and a plausible set of segments that cross the unknown area is identified. Then, a reconstruction algorithm is developed by combining sparse modeling and patch-based synthesis. The improved extrapolation capabilities of the presented approach is shown for variety of image characteristics and the robustness of the algorithm is illustrated for large unknown blocks, which are becoming especially important for future video coding standards in order to efficiently code high resolution content.