TY - JOUR
T1 - R-D performance upper bound of transform coding for 2-D directional sources
AU - Zhu, Shuyuan
AU - Yeung, Siu Kei Au
AU - Zeng, Bing
N1 - Funding Information:
Manuscript received April 26, 2009; revised June 10, 2009. First published June 23, 2009; current version published July 29, 2009. This work was supported in part by an RGC research grant of the HKSAR government. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Adrian Munteanu.
PY - 2009
Y1 - 2009
N2 - Traditionally, any 2-D transform (such as 2-D DCT) is implemented through two separable 1-D transforms along the vertical and horizontal dimensions. Such a framework is however not most suitable for a 2-D directional source in which the dominant directional information is neither horizontal nor vertical. In this letter, we attempt to determine the R-D performance upper bound for block-based transform coding schemes applied on such 2-D directional sources. It is not a surprise that the Karhunen-Loève transform (KLT) plays a critical role here. Specifically, we show that a nonseparableKLT can be determined directly from the given 2-D directional source model to yield the R-D performance upper bound. We also show that there exists a significant gap between this upper bound and the R-D performance that can be achieved by using the traditional 2-D DCT.
AB - Traditionally, any 2-D transform (such as 2-D DCT) is implemented through two separable 1-D transforms along the vertical and horizontal dimensions. Such a framework is however not most suitable for a 2-D directional source in which the dominant directional information is neither horizontal nor vertical. In this letter, we attempt to determine the R-D performance upper bound for block-based transform coding schemes applied on such 2-D directional sources. It is not a surprise that the Karhunen-Loève transform (KLT) plays a critical role here. Specifically, we show that a nonseparableKLT can be determined directly from the given 2-D directional source model to yield the R-D performance upper bound. We also show that there exists a significant gap between this upper bound and the R-D performance that can be achieved by using the traditional 2-D DCT.
KW - Discrete cosine transform
KW - Karhunen-Loève transform
KW - R-D performance
KW - Transform coding
UR - http://www.scopus.com/inward/record.url?scp=77956006786&partnerID=8YFLogxK
U2 - 10.1109/LSP.2009.2026115
DO - 10.1109/LSP.2009.2026115
M3 - Article
AN - SCOPUS:77956006786
SN - 1070-9908
VL - 16
SP - 861
EP - 864
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 10
M1 - 2026115
ER -