TY - GEN
T1 - Universal scanning of mixing random fields and the performance of the Peano-Hilbert scan
AU - Cohen, Asaf
AU - Merhav, Neri
AU - Weissman, Tsachy
PY - 2006/12/1
Y1 - 2006/12/1
N2 - We investigate the problem of scanning and prediction (" scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, where an image is compressed by coding the prediction error sequence resulting from scandicting it. Specifically, given a strongly mixing random field, we show that there exists a scandiction scheme which is independent of the field's distribution, yet almost surely asymptotically achieves the same performance as if this distribution was known. We then discuss the scenario where the Peano-Hilbert scanning order is used, accompanied by an optimal predictor, and derive a bound on the excess loss compared to optimal finite state scandiction, which is valid for any individual image and any bounded loss function.
AB - We investigate the problem of scanning and prediction (" scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, where an image is compressed by coding the prediction error sequence resulting from scandicting it. Specifically, given a strongly mixing random field, we show that there exists a scandiction scheme which is independent of the field's distribution, yet almost surely asymptotically achieves the same performance as if this distribution was known. We then discuss the scenario where the Peano-Hilbert scanning order is used, accompanied by an optimal predictor, and derive a bound on the excess loss compared to optimal finite state scandiction, which is valid for any individual image and any bounded loss function.
UR - http://www.scopus.com/inward/record.url?scp=50249139202&partnerID=8YFLogxK
U2 - 10.1109/EEEI.2006.321083
DO - 10.1109/EEEI.2006.321083
M3 - Conference contribution
AN - SCOPUS:50249139202
SN - 1424402301
SN - 9781424402304
T3 - IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings
SP - 62
EP - 66
BT - 2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, IEEEI
T2 - 2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, IEEEI
Y2 - 15 November 2006 through 17 November 2006
ER -