Abstract
In this chapter we sketch some rather elegant mathematical theorems that have had a significant impact on computational aspects of electrical engineering. We have used them over the years in performing eddy-current inversions and believe that they will have an expanded role to play in the future development of eddy-current NDE.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The discussion in this section follows [73], which should be consulted for the details.
- 2.
The order of the P i ’s is not important.
References
Herman, G.T., Lent, A., Hurwitz, H.: A storage-efficient algorithm for finding the regularized solution of a large, inconsistent system of equations. J. Inst. Math. Appl. 25, 361–366 (1980)
Herman, G.T., Meyer, L.B.: Algebraic reconstruction techniques can be made computationally efficient. IEEE Trans. Med. Imag. 12(3), 600–609 (September 1993)
Sabbagh, H.A., Sabbagh, L.D., Vernon, S.N.: Verification of an eddy-current flaw inversion algorithm. IEEE Trans. Magn. 22(6), 1881–1886 (November 1986)
Papoulis, A.: A new algorithm in spectral analysis and band-limited extrapolation. IEEE Trans. Circ. Syst. CAS-22, 735–742 (1975)
Youla, D.C.: Generalized image restoration by the method of alternating orthogonal projections. IEEE Trans. Circ. Syst. CAS-25, 694–702 (1978)
Youla, D.C., Webb, H.: Image restoration by the method of convex projections: Part 1-Theory. IEEE Trans. Med. Imag. MI-1, 81–94 (October 1982)
Lent, A., Tuy, H.: An iterative method for the extrapolation of band limited functions. J. Math. Anal. Appl. 83, 554–565 (1981)
Kaczmarz, S.: Angenaherte auflosung von systemen linearer gleichungen. Bull. Pol. Acad. Sci. Lett. A, 6–8A, 355–357 (1937)
Tanabe, K.: Projection method for solving a singular system. Numer. Math. 17, 203–214 (1971)
Hounsfield, G.N.: A method of and apparatus for examination of a body by radiation such as x-ray or gamma radiation. Patent Specification 1283915, The Patent Office (1972)
Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, New York (1988)
Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill, San Francisco (1968)
Pratt, W.K.: Digital Image Processing. Wiley, New York (1978).
Sabbagh, L.D., Sabbagh, H.A., Klopfenstein, J.S.: Image enhancement via extrapolation techniques: a two dimensional iterative scheme and a direct matrix inversion scheme. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 5, pp. 473–483. Plenum Press, New York (1986)
Sabbagh, H.A., Sabbagh, L.D., Roberts, T.M.: An eddy-current model and algorithm for three-dimensional nondestructive evaluation of advanced composites. IEEE Trans. Magn. 24(6), 3201–3212 (November 1988)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sabbagh, H.A., Murphy, R.K., Sabbagh, E.H., Aldrin, J.C., Knopp, J.S. (2013). Some Special Signal-Processing Algorithms. In: Computational Electromagnetics and Model-Based Inversion. Scientific Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8429-6_14
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8429-6_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-8428-9
Online ISBN: 978-1-4419-8429-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)