METHOD AND SYSTEM FOR HIGH-RESOLUTION TRANSFORMS OF FREQUENCY-SPACE AND IMAGE/AUDIO/VIDEO-SPACE DATA

摘要

A method and system for data processing and reconstruction, uses arbitrary frequency-space or image/audio/video-space (inverse frequency-space) sample points in N dimensions. According to a preferred embodiment of the invention, a subset of optionally pre-processed and pre-conditioned N-dimensional frequency-space (or image/audio/video-space) 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 image/audio/video-space (or frequency-space). Image/audio/video-space “color” data (or frequency-space data) are calculated (130) on a processor (361), preferably in parallel, at the x-coordinates corresponding to the horizontal keys. The image/audio/video-space coordinates (or the frequency-space coordinates) are arbitrary, and the reconstruction's calculated image/audio/video data (or the deconstruction's calculated frequency-space data) are optionally 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.

主权项

1. A method for medical, industrial, and multi-media frequency-space and image/audio/video-space data reconstruction or deconstruction, based on a data superset comprising a plurality of “N-dimensional starting-space sample points” (wherein “starting-space” is either frequency-space or “inverse frequency-space”), wherein optionally at least one of the “N-dimensional starting-space sample points” is pre-processed or pre-conditioned prior to or during implementation of the method, and wherein each “N-dimensional starting-space sample point” comprises a set of associated “sample-point component numbers” (each set of “sample-point component numbers” notated herein without loss of generality as {kx, ky, k3, k4, k5, . . . , kN; a, b}, wherein (kx, ky, k3, k4, k5, . . . , kN) is a “starting-space coordinate” and a+b√(−1) is a complex-number “starting-space data value” associated with the “starting-space coordinate” (kx, ky, k3, k4, k5, . . . , kN), and wherein a+b√(−1) is herein notated ), the method comprising:
(a) acquiring (102), by inputting, into a processing device (360), or storing, in a memory (363), a “starting-space data set” comprising a plurality of “starting-space sample points”, wherein each “starting-space sample point” comprises an element of the superset; (b) calculating, on a processor (361), for each of at least one x-coordinate in “target-space” (wherein each such “target-space x-coordinate” is arbitrary and is notated herein without loss of generality as px), an associated “horizontal key” res1 comprising at least one “horizontal key element”, wherein each “horizontal key element” is notated herein without loss of generality as res1i and comprises the sum∑z=r1r2(j2πkyi,zE1pxE2*〈ai,z,bi,z>)wherein j2=−1, r1 and r2 are arbitrary and the index z is arbitrary E1 and E2 are each an optional “region scaling factor”, kyi,z is one of the “sample-point component numbers” in the “starting-space data set”, is one of the “starting-space data values” in the “starting-space data set”, and wherein * represents complex-number multiplication;
(c) calculating, on the processor (361), for each of a plurality of arbitrary “target-space points” (wherein each such “target-space point” is notated herein without loss of generality as (px, py) and comprises a current “target-space x-coordinate” px and a current “target-space y-coordinate” py), a “color” (130), wherein the “color” comprises the sum∑i=r3r4(j2πpyE5kxiE6*res1i)wherein j2=−1, r3 and r4 are arbitrary and the index i is arbitrary, E5 and E6 are each an optional “region scaling factor”, kxi is the one of the “sample-point component numbers” in the “starting-space data set”, res1i is one of the “horizontal key elements” associated with at least one of the “horizontal keys” (preferably the “horizontal key” associated with the current “target-space x-coordinate” px), and wherein * represents complex-number multiplication; and
(d) forming (150), by storing, in the memory (363), or outputting, to a display device (367), or storing, on a storage device (366), or outputting, to an output device (365), “target-space data” comprising at least one of the “colors”.