The authors first propose an index mapping such that the type-IV in-dimensional discrete cosine transform (m-D DCT-IV) is turned into a sum involving a number of (m - 1)dimensional discrete cosine transforms ((m - 1)-...
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The authors first propose an index mapping such that the type-IV in-dimensional discrete cosine transform (m-D DCT-IV) is turned into a sum involving a number of (m - 1)dimensional discrete cosine transforms ((m - 1)-D DCTs). Then a polynomialtransform is used for implementing the sum. Based on symmetrical properties, a refined fast polynomial transform algorithm is proposed for computing the polynomialtransform. Compared to the row-column m-D DCT-IV algorithm, the proposed algorithm achieves remarkable savings in arithmetic operations. More precisely, the numbers of multiplications and additions for in-dimensional DCT-IV are nearly 1/m and (2m + 1)/3m times those of the row-column method, respectively.
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