Fast log-decon with a quasi-Newton solver |

In terms of convergence speed, it takes 35 iterations and 1.7 seconds for the L-BFGS technique to reach a minimum, and 123 iterations and 24 seconds for the steepest-descent algorithm (Figure 3). Ignoring the time it takes to read and write data on disk, each iteration of the L-BFGS algorithm is about five times faster, with almost four times less iterations. Clearly, this difference is not solely due to the better convergence properties of the quasi-Newton algorithm over the steepest-descent method. As mentioned before, different line-search strategies and stopping criteria matter as well.

Comp-cabo
Left: input data. Right: deconed data with the L-BFGS solver
Figure 1. |
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Comp-wvlt
Top: wavelet estimated with the L-BFGS method. Bottom: wavelet estimated with the steepest-descent method.
Figure 2. |
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Comp-fct
Convergence comparison between the steepest descent (solid) and L-BFGS (dash) methods. Note the narrow horizontal scale to highlight small differences close
to the convergence point.
Figure 3. | |
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Fast log-decon with a quasi-Newton solver |

2012-10-29