A class of partition-based interpolators that addresses a variety of image interpolation applications are proposed. The proposed interpolators first partition an image into a finite set of partitions that capture local image structures. Missing high resolution pixels are then obtained through linear operations on neighboring pixels that exploit the captured image structure. By exploiting the local image structure, the proposed algorithm produces excellent performance on both edge and uniform regions. The presented results demonstrate that partition-based interpolation yields results superior to traditional and advanced algorithms in the applications of color filter array (CFA) demosaicking and super-resolution reconstruction.