Hardware Design of the Discrete Wavelet Transform: an Analysis of Complexity, Accuracy and Operating Frequency

Dora Maria Ballesteros, Diego Renza, Luis Fernando Pedraza

Abstract


The purpose of this paper is to present a comparative analysis of hardware design of the Discrete Wavelet Transform (DWT) in terms of three design goals: accuracy, hardware cost and operating frequency. Every design should take into account the following facts: method (non-polyphase, polyphase and lifting), topology (multiplier-based and multiplierless-based), structure (conventional or pipelined), and quantization format (floatingpoint, fixed-point, CSD or integer). Since DWT is widely used in several applications (e.g. compression, filtering, coding, pattern recognition among others), selection of adequate parameters plays an important role in the performance of these systems.


Keywords


Discrete Wavelet Transform; method; topology; structure; quantization format

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Y. Zhang, Y. Wang, W. Wang, and B. Liu, “Doppler ultrasound signal denoising based on wavelet frames,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 48, no. 3, pp. 709–716, May 2001. [Online]. Available: http://ieeexplore.ieee.org/document/920698/ 130

D. Hepburn and M. Michel, “Second generation wavelet transform for data denoising in PD measurement,” IEEE Transactions on Dielectrics and Electrical Insulation, vol. 14, no. 6, pp. 1531–1537, Dec. 2007. [Online]. Available: http://ieeexplore.ieee.org/document/4401237/ 130

G. Bandyopadhyay, P. Syam, A. Chattopadhyay, and S. Das, “Application of Wavelet transform in denoising synchronising signal in line synchronised power electronics converters,” IET Power Electronics, vol. 5, no. 3, pp. 281–292, Mar. 2012. [Online]. Available: http://digital-library.theiet.org/content/journals/10.1049/iet-pel.2010.0382 130

J. Reichel, G. Menegaz, M. J. Nadenau, and M. Kunt, “Integer wavelet transform for embedded lossy to lossless image compression.” IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, vol. 10, no. 3, pp. 383–92, Jan. 2001. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/18249628 130

E. Hamid and Z.-I. Kawasaki, “Wavelet-based data compression of power system disturbances using the minimum description length criterion,” IEEE Transactions on Power Delivery, vol. 17, no. 2, pp. 460–466, Apr. 2002. [Online]. Available: http://ieeexplore.ieee.org/document/997918/ 130

B. A. Rajoub, “An efficient coding algorithm for the compression of ECG signals using the wavelet transform.” IEEE transactions on bio-medical engineering, vol. 49, no. 4, pp. 355–62, Apr. 2002. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/11942727 130

Y. Shi, “A DWT-DFT composite watermarking scheme robust to both affine transform and JPEG compression,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, no. 8, pp. 776–786, Aug. 2003. [Online]. Available: http://ieeexplore.ieee.org/document/1227607/ 130

L. Brechet, M.-F. Lucas, C. Doncarli, and D. Farina, “Compression of Biomedical Signals With Mother Wavelet Optimization and Best- Basis Wavelet Packet Selection,” IEEE Transactions on Biomedical Engineering, vol. 54, no. 12, pp. 2186–2192, Dec. 2007. [Online]. Available: http://ieeexplore.ieee.org/document/4360002/ 130

Y. Zheng, “Quality Constrained Compression Using DWT-Based Image Quality Metric,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 18, no. 7, pp. 910–922, Jul. 2008. [Online]. Available: http://ieeexplore.ieee.org/document/4472175/ 130

Z. Fang, N. Xiong, L. T. Yang, X. Sun, and Y. Yang, “Interpolation- Based Direction-Adaptive Lifting DWT and Modified SPIHT for Image Compression in Multimedia Communications,” IEEE Systems Journal, vol. 5, no. 4, pp. 584–593, Dec. 2011. [Online]. Available: http: //ieeexplore.ieee.org/document/6044698/ 130

H. Demirel and G. Anbarjafari, “Improved face recognition system using probability distribution functions extracted from wavelet subbands,” in 2009 24th International Symposium on Computer and Information Sciences, IEEE. Ankara: IEEE, Sep. 2009, pp. 94–98. [Online]. Available: http://ieeexplore.ieee.org/document/5291859/ 130

N. Begum, M. Alam, and M. I. Islam, “Application of Canny filter and DWT in fingerprint detection a new approach,” in 2010 13th International Conference on Computer and Information Technology (ICCIT), IEEE. Dhaka, Bangladesh: IEEE, Dec. 2010, pp. 256–260. [Online]. Available: http://ieeexplore.ieee.org/document/5723865/ 130

Y.-T. Chou, S.-M. Huang, S.-H. Wu, and J.-F. Yang, “DWT and Sub-pattern PCA for Face Recognition Based on Fuzzy Data Fusion,” in 2011 International Conference on Intelligent Computation and Bio-Medical Instrumentation, IEEE. Wuhan, China: IEEE, Dec. 2011, pp. 296–299. [Online]. Available: http://ieeexplore.ieee.org/document/6131767/ 130

R. Zhang and J. Ding, “Facial recognition based on wavelet transform,” in World Automation Congress (WAC), 2012. Puerto Vallarta, Mexico: IEEE, 2012, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/6321574/ 130

J. Andrew, “Coding gain and spatial localisation properties of discrete wavelet transform filters for image coding,” IEE Proceedings - Vision, Image, and Signal Processing, vol. 142, no. 3, p. 133, 1995. [Online]. Available: http://digital-library.theiet.org/content/journals/10.1049/ip-vis_19951938 130

D. Marpe and H. Cycon, “Very low bit-rate video coding using wavelet-based techniques,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 9, no. 1, pp. 85–94, 1999. [Online]. Available: http://ieeexplore.ieee.org/document/744277/ 130

S. Li and W. Li, “Shape-adaptive discrete wavelet transforms for arbitrarily shaped visual object coding,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 10, no. 5, pp. 725–743, 2000. [Online]. Available: http://ieeexplore.ieee.org/document/856450/ 130

K. Ferguson and N. Allinson, “Psychophysically derived quantisation model for efficient DWT image coding,” IEE Proceedings - Vision, Image, and Signal Processing, vol. 149, no. 1, p. 51, 2002. [Online]. Available: http: //digital-library.theiet.org/content/journals/10.1049/ip-vis_20020073 130

J. Yang, Y.Wang, W. Xu, and Q. Dai, “Image coding using dual-tree discrete wavelet transform.” IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, vol. 17, no. 9, pp. 1555–69, Sep. 2008. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/18701394 130

H. Mota, N. Volpini, G. Rodrigues, and F. Vasconcelos, “A realtime processing system for denoising of partial discharge signals using the wavelet transform,” in Conference Record of the 2008 IEEE International Symposium on Electrical Insulation, IEEE. Vancouver, British Colombia, Canada: IEEE, Jun. 2008, pp. 391–395. [Online]. Available: http://ieeexplore.ieee.org/document/4570356/ 130

J. Chilo and T. Lindblad, “Hardware Implementation of 1D Wavelet Transform on an FPGA for Infrasound Signal Classification,” IEEE Transactions on Nuclear Science, vol. 55, no. 1, pp. 9–13, 2008. [Online]. Available: http://ieeexplore.ieee.org/document/4448457/ 130

H. A. Darwish, M. Hesham, A.-M. I. Taalab, and N. M. Mansour, “Close Accord on DWT Performance and Real-Time Implementation for Protection Applications,” IEEE Transactions on Power Delivery, vol. 25, no. 4, pp. 2174–2183, Oct. 2010. [Online]. Available: http: //ieeexplore.ieee.org/document/5556054/ 130

J. d. J. Rangel-Magdaleno, R. d. J. Romero-Troncoso, R. A. Osornio-Rios, E. Cabal-Yepez, and A. Dominguez-Gonzalez, “FPGA-Based Vibration Analyzer for Continuous CNC Machinery Monitoring With Fused FFTDWT Signal Processing,” IEEE Transactions on Instrumentation and Measurement, vol. 59, no. 12, pp. 3184–3194, Dec. 2010. [Online]. Available: http://ieeexplore.ieee.org/document/5458093/ 130

K. Inoue, Y. Kuroki, M. Kurosaki, Y. Nagao, and H. Ochi, “Real time 2D-DWT of JPEG 2000 for Digital Cinema using CUDA 4.0,” in 2011 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS), IEEE. Chiang Mai, Thailand: IEEE, Dec. 2011, pp. 1–5. [Online]. Available: http://ieeexplore.ieee.org/document/6146127/ 130

Y. Han, H.-i. Kang, C. Kim, and Y. Seo, “Statistical Pattern Based Real-Time Smoke Detection Using DWT Energy,” in 2011 International Conference on Information Science and Applications, IEEE. Jeju Island in Korea: IEEE, Apr. 2011, pp. 1–7. [Online]. Available: http://ieeexplore.ieee.org/document/5772361/ 130

F. B. Costa, C. M. S. Neto, S. F. Carolino, R. L. A. Ribeiro, R. L. Barreto, T. O. A. Rocha, and P. Pott, “Comparison between two versions of the discrete wavelet transform for real-time transient detection on synchronous machine terminals,” in 2012 10th IEEE/IAS International Conference on Industry Applications, IEEE. Fortaleza, CE: IEEE, Nov. 2012, pp. 1–5. [Online]. Available: http://ieeexplore.ieee.org/document/6453533/ 130

D. M. Ballesteros, D. M. Moreno, and A. E. Gaona, “FPGA compression of ECG signals by using modified convolution scheme of the Discrete Wavelet Transform,” Ingeniare. Revista chilena de ingeniería, vol. 20, no. 1, pp. 8–16, Apr. 2012. [Online]. Available: http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0718-33052012000100002&lng=en&nrm=iso&tlng=en 130, 139

D. M. Ballesteros L and J. M. Moreno A, “Wavelet-denoising on hardware devices with Perfect Reconstruction, low latency and adaptive thresholding,” Computers & Electrical Engineering, vol. 39, no. 4, pp. 1300–1311, May 2013. [Online]. Available: http://linkinghub.elsevier.com/retrieve/pii/S0045790613000621 130, 135, 137, 138, 139, 140

——, “Real-time, speech-in-speech hiding scheme based on least significant bit substitution and adaptive key,” Computers & Electrical Engineering, vol. 39, no. 4, pp. 1192–1203, May 2013. [Online]. Available: http://linkinghub.elsevier.com/retrieve/pii/S0045790613000323 130, 132, 135,137, 138, 139

K. Kotteri, S. Barua, A. Bell, and J. Carletta, “A comparison of hardware implementations of the biorthogonal 9/7 DWT: convolution versus lifting,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 52, no. 5, pp. 256–260, May 2005. [Online]. Available: http://ieeexplore.ieee.org/document/1431103/ 130, 139, 140

K. Kotteri, A. Bell, and J. Carletta, “Multiplierless filter Bank design: structures that improve both hardware and image compression performance,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 16, no. 6, pp. 776–780, Jun. 2006. [Online]. Available: http://ieeexplore.ieee.org/document/1637517/ 130, 139, 140

H. Li, Q. Wang, and L. Wu, “A novel design of lifting scheme from general wavelet,” IEEE Transactions on Signal Processing, vol. 49, no. 8, pp. 1714– 1717, 2001. [Online]. Available: http://ieeexplore.ieee.org/document/934141/130

A. Soman and P. Vaidyanathan, “On orthonormal wavelets and paraunitary filter banks,” IEEE Transactions on Signal Processing, vol. 41, no. 3, pp. 1170–1183, Mar. 1993. [Online]. Available: http://ieeexplore.ieee.org/ document/205722/ 130

X. Lan, N. Zheng, and Y. Liu, “A high-performance and memoryefficient VLSI architecture with parallel scanning method for 2-D lifting-based discrete wavelet transform,” IEEE Transactions on Consumer Electronics, vol. 55, no. 2, pp. 400–407, May 2009. [Online]. Available: http://ieeexplore.ieee.org/document/5174400/ 130

D.-U. Lee, L.-W. Kim, and J. D. Villasenor, “Precision-aware selfquantizing hardware architectures for the discrete wavelet transform.” IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, vol. 21, no. 2, pp. 768–77, Feb. 2012. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/21824849 130, 139

S. Silva and S. Bampi, “Area and Throughput Trade-Offs in the Design of Pipelined DiscreteWavelet Transform Architectures,” in Design, Automation and Test in Europe, IEEE. Grenoble, France: IEEE, 2005, pp. 32–37. [Online]. Available: http://ieeexplore.ieee.org/document/1395789/ 130, 139

Y.-K. Lai, L.-F. Chen, and Y.-C. Shih, “A high-performance and memory-efficient VLSI architecture with parallel scanning method for 2-D lifting-based discrete wavelet transform,” IEEE Transactions on Consumer Electronics, vol. 55, no. 2, pp. 400–407, May 2009. [Online]. Available: http://ieeexplore.ieee.org/document/5174400/ 130, 139

M. A. Farahani, S. Mirzaei, and H. A. Farahani, “Implementation of a reconfigurable architecture of discrete wavelet packet transform with three types of multipliers on FPGA,” in 2011 24th Canadian Conference on Electrical and Computer Engineering(CCECE), IEEE. Niagara Falls, Ontario: IEEE, May 2011, pp. 001 459–001 462. [Online]. Available: http://ieeexplore.ieee.org/document/6030704/ 130

Z. Szadkowski, “An Optimization of the FPGA Based Wavelet Trigger in Radio Detection of Cosmic Rays,” IEEE Transactions on Nuclear Science, vol. 62, no. 3, pp. 993–1001, Jun. 2015. [Online]. Available: http://ieeexplore.ieee.org/document/7102787/ 130

K. Kotteri, A. Bell, and J. Carletta, “Design of Multiplierless, High- Performance, Wavelet Filter Banks With Image Compression Applications,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 3, pp. 483–494, Mar. 2004. [Online]. Available: http://ieeexplore.ieee.org/document/1275595/ 130, 139

W. Wang, Z. Du, and Y. Zeng, “High-Speed FPGA Implementation for DWT of Lifting Scheme,” in 2009 5th International Conference on Wireless Communications, Networking and Mobile Computing, IEEE. Beijing, China: IEEE, Sep. 2009, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/5302003/ 130, 139, 140

G. N. Geetha and K. K. Mohammed Salih, “A parallel processing architecture for two dimensional discrete wavelet transform without using multipliers,” in 2012 Third International Conference on Computing, Communication and Networking Technologies (ICCCNT’12), IEEE. Tamilnadu, India: IEEE, Jul. 2012, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/6396059/ 130, 139

A. Abbas and T. Tran, “Multiplierless Design of Biorthogonal Dual-Tree Complex Wavelet Transform using Lifting Scheme,” in 2006 International Conference on Image Processing, IEEE. Atlanta, GA: IEEE, 2006, pp. 1605– 1608. [Online]. Available: http://ieeexplore.ieee.org/document/4106852/130, 139

——, “Rational Coefficient Dual-Tree Complex Wavelet Transform: Design and Implementation,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3523–3534, Aug. 2008. [Online]. Available: http://ieeexplore.ieee.org/document/4527184/ 130, 139

M. Zhang, R. Deng, Z. Ma, and M. Zhang, “A FPGA-based low-cost realtime wavelet packet denoising system,” in Proceedings of 2011 International Conference on Electronics and Optoelectronics, vol. 2, IEEE. Dalian, Liaoning, China: IEEE, Jul. 2011, pp. V2–350–V2–353. [Online]. Available: http://ieeexplore.ieee.org/document/6013254/ 130, 139

N. Elghamery and S.-D. Habib, “An efficient FPGA implementation of a wavelet coder/decoder,” in ICM 2000. Proceedings of the 12th International Conference on Microelectronics. (IEEE Cat. No.00EX453), IEEE. Singapore City, Singapore: Univ. Tehran, 2000, pp. 269–272. [Online]. Available: http://ieeexplore.ieee.org/document/916458/ 130

J. M. Abdul-Jabbar and R. W. Hmad, “Allpass-based design, multiplierless realization and implementation of IIR wavelet filter banks with approximate linear phase,” in International Symposium on Innovations in Information and Communications Technology, IEEE. Amman Jordan: IEEE, Nov. 2011, pp. 118–123. [Online]. Available: http://ieeexplore.ieee.org/document/6149606/130

S. Ghosh, S. P. Maity, and H. Rahaman, “Multiplier-less VLSI architecture of 1-D Hilbert transform pair using Biorthogonal Wavelets for QCM-SS image watermarking,” in 2013 4th International Conference on Computer and Communication Technology (ICCCT), IEEE. Allahabad, India: IEEE, Sep. 2013, pp. 5–10. [Online]. Available: http://ieeexplore.ieee.org/document/6749594/ 130

T.-Y. Sung, Y.-S. Shieh, C.-W. Yu, and H.-C. Hsin, “Low-Power Multiplierless 2-D DWT and IDWT Architectures Using 4-tap Daubechies Filters,” in 2006 Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT’06), IEEE. Taipei, Taiwan: IEEE, 2006, pp. 185–190. [Online]. Available: http://ieeexplore.ieee.org/document/4032175/ 130

C. Zhang, C. Wang, and M. O. Ahmad, “A Pipeline VLSI Architecture for Fast Computation of the 2-D Discrete Wavelet Transform,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 8, pp. 1775–1785, Aug. 2012. [Online]. Available: http://ieeexplore.ieee.org/document/6133304/ 130

K. Mei, N. Zheng, and Y. Liu, “A high pipeline and low memory design of JPEG2000 encoder,” in Proceedings of the Ninth International Symposium on Consumer Electronics, 2005. (ISCE 2005)., IEEE. Quebec, canada: IEEE, 2005, pp. 315–319. [Online]. Available: http://ieeexplore.ieee.org/document/1502394/ 130

X. Fan, Z. Pang, D. Chen, and H. Z. Tan, “A Pipeline Architecture for 2-D Lifting-Based Discrete Wavelet Transform of JPEG2000,” in 2010 International Conference on Multimedia Technology, IEEE. Xuanwu, china: IEEE, Oct. 2010, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/5629864/ 130

X. Mei-hua, C. Zhang-jin, R. Feng, and C. Yu-lan, “Architecture research and VLSI implementation for discrete wavelet packet transform,” in Conference on High Density Microsystem Design and Packaging and Component Failure Analysis, 2006. HDP’06., IEEE. Shanghai, China: IEEE, 2006, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/1707554/ 130

M. Maamoun, R. Bradai, A. Meraghni, and R. Beguenane, “Low cost VLSI discrete wavelet transform and FIR filters architectures for very high-speed signal and image processing,” in 2010 IEEE 9th International Conference on Cyberntic Intelligent Systems, IEEE. Reading, United Kingdom: IEEE, Sep. 2010, pp. 1–6. [Online]. Available: http://ieeexplore.ieee.org/document/5898088/ 130, 140

Z. Wu and W. Wang, “Pipelined architecture for FPGA implementation of lifting-based DWT,” in 2011 International Conference on Electric Information and Control Engineering. Yichang, China: IEEE, Apr. 2011, pp. 1535–1538. [Online]. Available: http://ieeexplore.ieee.org/document/5777731/ 130, 140

M. Nagabushanam, P. Cyril Prasanna Raj, and S. Ramachandran, “Design and FPGA implementation of modified Distributive Arithmetic based DWT-IDWT processor for image compression,” in 2011 International Conference on Communications and Signal Processing, IEEE. Nanjing, China: IEEE, Feb. 2011, pp. 1–4. [Online]. Available: http://ieeexplore.ieee.org/document/5739397/ 140




DOI: http://dx.doi.org/10.17230/ingciencia.12.24.6

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