1. A system for numerical image formation and for refinement from overlapping measurement vignettes captured by an image sensor array with associated micro-optical arrangements, the system comprising: an image sensor comprising the plurality of micro-optical arrangements that creates a plurality of light detection signals in response to a plurality of optically vignetted portions of an incoming light field associated with an observed scene, wherein each of the plurality of optically vignetted portions is produced by individual ones of the micro-optical arrangements; a multiplexing arrangement for gathering said plurality of light detection signals into a stream of measurement values responsive to an incoming light field associated with an observed scene; a processor for receiving the stream of measurement values, the processor executing a numerical image formation algorithm comprising linear mathematical transformations on the stream of measurement values to produce at least one synthesized digital image; and an output for transferring said at least one synthesized digital image to an external system; wherein the processor produces a visual image responsive to the incoming light field associated with the observed scene.