Methods, systems, and apparatus, including computer programs encoded on computer storage media, for supporting large lookup tables on an image processor. One of the methods includes receiving an input kernel program for an image processor having a two-dimensional array of execution lanes, a shift-register array, and a plurality of memory banks. If the kernel program has an instruction that reads a lookup table value for a lookup table partitioned across the plurality of memory banks, the instruction in the kernel program are replaced with a sequence of instructions that, when executed by an execution lane, causes the execution lane to read a first value from a local memory bank and a second value from the local memory bank on behalf of another execution lane belonging to a different group of execution lanes.