Algebraic integer architecture with minimum adder count for the 2-D Daubechies 4-tap filters banks
- 211 Downloads
A multiplierless architecture based on algebraic integer representation for computing the Daubechies 4-tap wavelet transform for 1-D/2-D signal processing is proposed. This architecture improves on previous designs in a sense that it minimizes the number of parallel 2-input adder circuits. The algorithm was achieved using numerical optimization based o exhaustive search over the algebraic integer representation. The proposed architecture furnishes exact computation up to the final reconstruction step, which is the operation that maps the exactly computed filtered results from algebraic integer representation to fixed-point. Compared to Madishetty et al. (IEEE Trans Circuits Syst I (Accepted, In Press), 2012a), this architecture shows a reduction of \(10\cdot n-3\) adder circuits, where \(n\) is the number of wavelet decomposition levels. Standard \(512\times 512\) images Mandrill, Lena, and Cameraman were submitted to digital realizations of both proposed algebraic integer based as well as fixed-point schemes, leading to quantifiable comparisons. The design is physically implemented for a 4-level 2-D decomposition using a Xilinx Virtex-6 vcx240t-1ff1156 FPGA device operating at up to a maximum clock frequency of 263.15 MHz. The FPGA implementation is tested using hardware co-simulation using an ML605 board with clock of 100 MHz. A 45 nm CMOS synthesis shows improved clock frequency of better than 500 MHz for a supply voltage of 1.1 V.
KeywordsAlgebraic integer encoding Daubechies wavelets Error-free algorithm Subband coding
This work was supported by the University of Akron, Ohio, USA; the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CPNq) and FACEPE, Brazil; and the Natural Science and Engineering Research Council (NSERC), Canada.
- Athar, S., & Gustafsson, O. (2011). Optimization of AIQ representations for low complexity wavelet transforms. In Proceedings of 20th European conference circuit theory and design (ECCTD) (pp. 314–317). doi: 10.1109/ECCTD.2011.6043349.
- Games, R. A., O’Neil, S. D., & Rushanan, J. J. (1988). Algebraic integer quantization and conversion. Tech. rep., Rome Air Development Center, Griffiss Air Force Base, NY 13441–5700.Google Scholar
- ImageProcessingPlacecom. (2012). Image databases. http://www.imageprocessingplace.com/root_files_V3/image_databases.htm.
- Islam, M. A., & Wahid, K. A. (2010). Area- and power-efficient design of Daubechies wavelet transforms using folded AIQ mapping. IEEE CAS II: Express Briefs, 57(9), 716–720.Google Scholar
- Madishetty, S., Madanayake, A., Cintra, R. J., Dimitrov, V., & Mugler, D. (2012a). VLSI architecture for Daubechies 4-tap and 6-tap wavelet filters using algebraic integers. IEEE Transactions on Circuits and Systems I, 60, 1455–1468.Google Scholar
- Madishetty, S., Madanayake, A., Cintra, R. J., Mugler, D., & Dimitrov, V. (2012b). Error-free VLSI architecture for Daubechies 4-tap filter using algebraic integers. In ISCAS (pp. 1484–1487).Google Scholar
- Misiti, M., Misiti, Y., Oppenheim, G., & Poggi, J. M. (2011). Wavelet toolbox user’s guide. Natick, MA: Mathworks, Inc.Google Scholar
- Murugesan, S., & Tay, D. B. H. (2011). New techniques for rationalizing orthogonal and biorthogonal wavelet filter coefficients. IEEE Transactions on Circuits and Systems, 59, 628–637.Google Scholar
- Skodras, A., Christopoulos, C., & Ebrahimi, T. (2001). The JPEG 2000 still image compression standard. IEEE Signal Processing Magazine, 18, 36–58.Google Scholar
- Wahid, K. A. (2011). Low complexity implementation of Daubechies wavelets for medical imaging applications, Chapter 8. In Discrete wavelet transforms—algorithms and applications (pp. 121–134). InTech.Google Scholar
- Wahid, K. A., Dimitrov, V. S., Jullien, G. A., & Badawy, W. (2002a). An algebraic integer based encoding scheme for implementing Daubechies discrete wavelet transforms. In Asilomar conference onf signals, systems and computers (Vol. 1, pp. 967–971). doi: 10.1109/ACSSC.2002.1197320.
- Wahid, K. A., Dimitrov, V. S., Jullien, G. A., & Badawy, W. (2002b). An analysis of Daubechies discrete wavelet transform based on algebraic integer encoding scheme. In Proceedins of third international workshop digital and computational video DCV, 2002, pp. 27–34. doi 10.1109/DCV.2002.1218740.
- Wahid, K. A., Dimitrov, V. S., & Jullien, G. A. (2003a). Error-free arithmetic for discrete wavelet transforms using algebraic integers. In: Proceedings of the 16th IEEE symposium on computer arithmetic (pp. 238–244). doi: 10.1109/ARITH.2003.1207684.
- Wahid, K. A., Islam, M. A., & Ko, S. B. (2011). Lossless implementation of Daubechies 8-tap wavelet transform. In Proceedings of the IEEE international symposium on circuits and systems, Rio de Janeiro, Brazil, (pp. 2157–2160). doi: 10.1109/ISCAS.2011.5938026.