NON-ITERATIVE METHOD TO RESTORE IMAGE FROM TRANSFORMED COMPONENT DATA

An original image or other data sequence is modified with an internal marker value, and is communicated (stored and/or transmitted) as one component of a transform having multiple complementary components. The image is restored in a closed form, without iteration, and in some cases without any loss of precision from the original image. The original image may have complex element values. Multiple original images may be combined, and separated after restoration. Several types of maps may be embedded in or packaged with the communicated component. Communicated component elements may be stored with variable lengths.