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

EURASIP Journal on Image and Video Processing

Table 1 The list of popular and known from the literature approximations of 8-point DCT

Short name	Introduced by	No. of additions	No. of shifts	Orthogonality
SDCT2001	Haweel in [6]	24	0	-
BAS2008I	Bouguezel et al. in [7]	18	2	+
BAS2008II	Bouguezel et al. in [8]	21	0 (3) ^∗	-
BAS2010	Bouguezel et al. in [10]	24	4	+
BAS2011 (a=\(\{0,\frac {1}{2},1\}\))	Bouguezel et al. in [9]	16/18/18	0/2/0	+
CB2011	Cintra and Bayer [11]	22	0	-
BC2012	Bayer and Cintra [12]	14	0	+
PMCBR2012	Potluri et al. in [15]	24	6	+
PS2012	Puchala and Stokfiszewski in [13]	18	2	+
DR2014	Dhandapani and Ramachandran in [5]	12	0	-
PMCBKE2014	Potluri et al. in [16]	14	0	+

^*The value in brackets indicate the number of operations required in the case of an inverse transformation. It should be noted that approximation BAS2011 is parametrized with the value of one parameter a. In this paper, we consider three values \(a=\{0,\frac {1}{2},1\}\) (also considered in the original paper [9]) which results in three sets of the numbers of additions and bit-shift operations