New algorithms are proposed for the type-III multidimensionalndiscrete cosine transform (MD-DCT-III). The polynomial transform is usednto convert the type-III MD-DCT into a series of one-dimensional type-IIIndiscrete cosine transforms (1-D-DCT-III). The algorithms achievenconsiderable savings on the number of operations compared to the rowncolumn method. For computing an r-dimensional DCT-III, the number ofnmultiplications required by the proposed algorithm is only 1/Τ timesnthat needed by the row-column method, and the number of additions isnalso reduced. Compared to other known fast algorithms forntwo-dimensional- and MD-DCTs, the proposed method uses about the samennumber of operations. However, advantages such as better computationalnstructure and flexibility on the choice of dimensional sizes can benachieved
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