Approximate calculation of 8-point DCT for various scenarios of practical applications

EURASIP Journal on Image and Video Processing

Table 6 The results of analysis of known approximations of DCT in the case of the symmetric scenario (π(V)=0.131042)

Type	Adds	Shifts	\(\chi _{3}(U,\overline {U})\)	\(\epsilon _{A}^{(III)}(U,\overline {U})\)	\(\text {tr}(\overline {U}^{T}\overline {U})/N\)	π(U)	Orthogonality
DR2014	12	0	5.782034	0.000000	3.000000	0.542537	-
			(2.545508)^∗	(1.100000)^∗	(0.750000)^∗
BC2012	14	0	0.656552	0.000000	1.000000	0.184816	+
PMCBKE2014	14	0	0.656552	0.000000	1.000000	0.184816	+
BAS2008III (a=0.0)	16	0	0.574577	0.000000	1.000000	0.161740	+
BAS2008III (a=1.0)	18	0	0.574474	0.000000	1.000000	0.161711	+
BAS2008III (a=0.5)	18	2	0.547763	0.000000	1.000000	0.154192	+
BAS2008I	18	2	0.547763	0.000000	1.000000	0.154192	+
PS2012	18	2	0.534894	0.000000	1.000000	0.150570	+
BAS2008II	21	0	1.032007	0.000000	1.781250	0.163090	-
			(0.794446)^∗	(0.215074)^∗	(1.000000)^∗
CB2011	22	0	0.539839	0.000000	1.000000	0.151962	+
SDCT2001	24	0	0.886988	0.000000	1.500000	0.166455	-
			(0.951579)^∗	(0.360253)^∗	(1.000000)^∗
BAS2010	24	4	0.522419	0.000000	1.000000	0.147058	+
PMCBR2012	24	6	0.520192	0.000000	1.000000	0.146431	+

^*Values in parentheses describe results obtained with \(\overline {U}=U^{T}\); otherwise we have \(\overline {U}=U^{-1}\).