A method and system for high-resolution and parallelizable data processing, reconstruction, and deconstruction, uses arbitrary frequency-space (FS) or inverse frequency-space (IFS, such as image, audio, or video space) sample points in N dimensions. According to a preferred embodiment of the invention, a subset of optionally pre-processed and/or pre-conditioned N-dimensional FS data (or IFS data) is acquired (102) by a processing device (360), the data is optionally transformed (115) by “region scaling factors”, and the data is optionally reduced (116) in numerical significant digits. A “horizontal key” of data elements is calculated (120) on a processor (361), preferably in parallel, for each of an arbitrary set of x-coordinates in IFS (or FS). IFS “color” data (or FS data) are calculated (130) on a processor (361), preferably in parallel, at the x-coordinates corresponding to the horizontal keys. The IFS coordinates (or the FS coordinates) are arbitrary, and the reconstruction's calculated IFS data (or the deconstruction's calculated FS data) are optionally rotated or transposed (141) (such as for display purposes), and are thus formed (150) in a memory (363) or on an output device (365). The method can be applied to other subsets, such as in the N-dimensional case.