A novel split-radix fast algorithm for 2-D discrete Hartley transform

Authors:
Longyu Jiang;Huazhong Shu;Jiasong Wu;Lu Wang;Lotfi Senhadji
Affiliations:
Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing, China;Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing, China and Centre de Recherche en Information Biomédicale Sino-Franç ...;Lab. of Image Sci. and Techn., School of Biological Sci. and Medical Eng., Southeast Univ., Nanjing, China and INSERM, Rennes, France and Univ. de Rennes 1, France and Centre de Recherche en Inf. ...;Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing, China and Centre de Recherche en Information Biomédicale Sino-Franç ...;INSERM, Rennes, France and Laboratoire Traitement du Signal et de l'Image, Université de Rennes 1, Rennes, France and Centre de Recherche en Information Biomédicale Sino-Français, R ...
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

This paper presents a fast split-radix-(2×2)/(8×8) algorithm for computing the 2-D discrete Hartley transform (DHT) of length with 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 48 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.