High Performance Design Of Linear Algebra Operations For Image Processing In Fpga Implementation
Keywords:FPGA, Convolution filter, Matrix multiplication.
Numerical linear algebra operations are key primitives in scientific computing. In this paper, performance optimizations of linear algebraic operations have been extensively investigated. FPGA-based high-performance designs are proposed for dot product, matrix-vector multiplication and matrix multiplication by identifying the parameters for each operation and analyzing the trade-offs. It is proposed to implement dot product in convolution filter, which is useful in noise removal, and Matrix multiplication in boundary tracing, which is useful for shape analysis and calculating geometric features. These high performance designs of linear algebra applications are proposed to be implemented on Xilinx FPGAs.
2. Underwood K.D. and Hemmert K.S. (2004), ‘Closing the Gap: CPU and FPGA Trends in Sustainable Floating-Point BLAS Performance’, Proc. 12th Ann. IEEE Symp. Field- Programmable Custom Computing Machines, Apr. 2004.
3. Smith M., Vetter J. and. Liang X (2005), ‘Accelerating Scientific Applications with the SRC-6 Reconfigurable Computer: Methodologies and Analysis’, Proc. 19th IEEE Int’l Parallel and Distributed Processing Symp., Apr. 2005.
4. Guo Z., Najjar W., Vahid F. and Vissers K. (2004), ‘A Quantitative Analysis of the Speedup Factors of FPGAs over Processors’, Proc.12th ACM/SIGDA Int’l Symp. Field Programmable Gate Arrays, Feb. 2004, pp. 162-170.
5. Aggarwal V., George A. and Slatton K. (2006), ‘Reconfigurable Computing with Multiscale Data Fusion for Remote Sensing’, Proc. 14th ACM/SIGDA Int’l Symp. Field Programmable Gate Arrays, Feb. 2006, p. 235.
6. Bajracharya S., Shu C., Gaj K. and El-Ghazawi T. (2004), ‘Implementation of Elliptic Curve Cryptosystems over gfð2nÞ in Optimal Normal Basis on a Reconfigurable Computer’, Proc. 12th ACM/SIGDA Int’l Symp. Field Programmable Gate Arrays, Feb. 2004.
7. Buell D.A. and Davis J.P. (2002), ‘Reconfigurable Computing Applied to Problems in Communications Security’, Proc. Fifth Ann. Int’l Conf. Military and Aerospace Programmable Logic Devices, Sept. 2002.
8. Koohi A., Bagherzadeh N. and Pan C. (2003), ‘A Fast Parallel Reed-Solomon Decoder on a Reconfigurable Architecture’, Proc. First IEEE/ACM/IFIP Int’l Conf. Hardware/Software Codesign and System Synthesis, Oct. 2003.
9. Bader D., Moret B. and Sanders P. (2002), ‘High-Performance Algorithm Engineering for Parallel Computation’, Lecture Notes in Computer Science, Vol. 2547, pp. 1-23..
10. Lawson C., Hanson R., Kincaid D. and Krogh F. (1979), ‘Basic Linear Algebra Subprograms for FORTRAN Usage’, ACM Trans. Math. Software, Vol. 5, No. 3, pp. 308-323.
11. Zhuo L. and Prasanna V.K. (2004), ‘Scalable and Modular Algorithms for Floating- Point Matrix Multiplication on FPGAs’, Proc. 18th Int’l Parallel and Distributed Processing Symp., Apr. 2004.
12. Smith M., Vetter J. and Alam S. (2005), ‘Scientific Computing Beyond CPUs: FPGA Implementations of Common Scientific Kernels’, Proc. Eighth Ann. Int’l Conf. Military and Aerospace Programmable Logic Devices, Sept. 2005.
13. Barrett R., Berry M., Chan T.F., Demmel J., Donato J., Dongarra J., Eijkhout V., Pozo R., Romine C. and der Vorst H.V. (1994), Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, second ed. SIAM, 1994.
14. Press W.H., Flannery B.P., Teukolsky S.A. and Vetterling W.T. (1992), Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press, 1992. IEEE 754 Standard for Binary Floating-Point Arithmetic, IEEE, 1984. Whaley R.C., Petitet A. and Dongarra J.J. (2001), ‘Automated Empirical Optimization of Software and the ATLAS Project’, Parallel Computing, also available as Univ. of Tennessee LAPACK Working Note #147, UT-CS-00-448, 2000.
Authors need to sign following agreement with International Journal of MC Square Scientific Research before publishing their articles:
- Authors need to return copyright form to Journal Editor-in-chief to proceed their articles for publication. Meantime, the journal licensed under a Creative Commons Attribution License, which permits other user to distribute the work with an acknowledgement of the authors for International Journal of MC Square Scientific Research.
- Authors are also able to share their separate, additional contractual arrangements for the non-restricted contribution of the journal with an acknowledgement of publication in International Journal of MC Square Scientific Research.
- Authors are allowed and encouraged to share their work during the submission process for increasing citation and exploring to increase the paper availability in worldwide way. The Effect of Open Access.