A fast algorithm for the 4x4 discrete Krawtchouk transform

J. S. Wu (1, 2) , C. F. Yang (1, 2) , H. Z. Shu (1, 2) , L. Wang (1, 2) , L. Senhadji (3)

1 LIST - Laboratory of Image Science and Technology [Nanjing]
2 CRIBS - Centre de Recherche en Information Biomédicale sino-français
3 LTSI - Laboratoire Traitement du Signal et de l'Image

A fast algorithm for computing the 4x4 discrete Krawtchouk transform (DKT) is proposed. By exploiting the reduced number of different values of basis functions, the proposed algorithm decreases significantly the number of arithmetic operations. It requires only 8 multiplications, 80 additions and 32 shifts, which saves about 98%, 88% and 83% multiplications compared to the direct method, the method using the properties of the DKT and the method computed by cascaded digital filters, respectively. The - proposed - algorithm could be used to efficiently compute the building-blocks when the process of the large image size is performed. Experiments are provided to demonstrate the efficiency of the proposed algorithm.

Keywords: image-analysis; computation; moments; compression; cosine; dct

Domains: Life Sciences [q-bio]; Bioengineering

J. S. Wu, C. F. Yang, H. Z. Shu, L. Wang, L. Senhadji. A fast algorithm for the 4x4 discrete Krawtchouk transform. Wan, Y and Shao, L and Wang, L and Sun, J and Nan, J and Zhang, Q. CRC PRESS-TAYLOR & FRANCIS GROUP, pp.23--28, 2015, 978-1-315-68858-9; 978-1-138-02785-5. ⟨hal-01380116⟩