A Novel Split-Radix Fast Algorithm for 2-D Discrete Hartley Transform

Longyu Jiang (1) , Huazhong Shu (1, 2) , Jiasong Wu (1, 2, 3) , Lu Wang (1, 2) , Lotfi Senhadji (2, 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

This paper presents a fast split-radix-(2×2)/(8×8) algorithm for computing the two-dimensional (2-D) discrete Hartley transform (DHT) of length N×N with N = q*2m, where q is an odd integer. The proposed algorithm decomposes an N×N DHT into one N/2×N/2 DHT and forty-eight N/8×N/8 DHTs. It achieves an efficient reduction on the number of arithmetic operations, data transfers and twiddle factors compared to the split-radix-(2×2)/(4×4) algorithm. Moreover, the characteristic of expression in simple matrices leads to an easy implementation of the algorithm. If implementing the above two algorithms with fully parallel structure in hardware, it seems that the proposed algorithm can decrease the area complexity compared to the split-radix-(2×2)/(4×4) algorithm, but requires a little more time complexity. An application of the proposed algorithm to 2-D medical image compression is also provided.

Mots clés: Two-dimensional (2-D) discrete Hartley transform (DHT); split-radix; fast algorithm; data compression

Domaines: Traitement du signal et de l'image [eess.SP]; Ingénierie biomédicale; Théorie des représentations [math.RT]; Imagerie; Traitement du signal et de l'image [eess.SP]

Longyu Jiang, Huazhong Shu, Jiasong Wu, Lu Wang, Lotfi Senhadji. A Novel Split-Radix Fast Algorithm for 2-D Discrete Hartley Transform. IEEE Transactions on Circuits and Systems Part 1 Fundamental Theory and Applications, 2010, 57 (4), pp.911-924. ⟨10.1109/TCSI.2009.2028639⟩. ⟨inserm-00405223⟩