1. A method for generating a resulting image comprising the steps of: (a) partitioning image data into blocks, each block including edge pixels located along a boundary and remaining pixels; (b) processing each block by: (i) computing an estimated orientation of a discontinuity edge within each block by evaluating through ray tracing the edge pixels; (ii) interpolating the remaining pixels from the evaluated edge pixels through a finite element approximation; and wherein the resulting image is produced when processing of the blocks has been completed.