28 May 2004 Parameterized reversible integer discrete cosine transforms
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In this paper a general parameterized integer-to-integer discrete cosine transform (DCT) is introduced. The parameter of the transform relates to the operation of floor function. The traditional method of integer transforms is based on the use of floor function by adding number 0.5 in each stage of the integer transform calculation. We consider the integer DCT with other parameters to be chosen in an optimal way. The optimality is with respect to the minimal mean-square-error of the integer DCT compared with the original DCT with the float-point multiplication. And while achieving the minimum error we are able to reconstruct the inputs exactly. Examples for the 2-, 4-, and 8-point integer reversible and inverse DCTs of types II and IV are analyzed in detail and optimal parameters for estimation of these transforms by integer DCTs are defined.
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Veerabhadra S Bhamidipati, Veerabhadra S Bhamidipati, Artyom M. Grigoryan, Artyom M. Grigoryan, } "Parameterized reversible integer discrete cosine transforms", Proc. SPIE 5298, Image Processing: Algorithms and Systems III, (28 May 2004); doi: 10.1117/12.525733; https://doi.org/10.1117/12.525733

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