The inversion of a linear transformation requires a stable algorithm. The algorithm should also permit regularization for noisy measurement data. The singular-value decomposition satisfies these requirements at a significant computational cost. We propose that bidiagonalization of the transformation also achieves the desired characteristics but at a much lower cost. We employ a modified Lanczos method rather than Householder transformations, as this method produces the basis vectors more directly and is more suitable for our exposition. We demonstrate the method with data previously used in the literature.
© 1988 Optical Society of America
M. C. Jones and C. H. Travis, "Bidiagonalization for linear inverse problems," J. Opt. Soc. Am. A 5, 660-665 (1988)