L-curve

L-Curve tab

(This step is optional)

The L-Curve lets you explore the result as a function of regularization parameter (alpha, smoothness). There is also a graph of the two norms vs. alpha. It can be calculated for Tikhonov regularization (plain or non-negative) or for the fitting algorithm.

Remember to constrain the distance range on the distance tab using the yellow cursors to exclude regions without significant peaks to speed up the calculations. After the L-curve is calculated, you can grab the green cursor in the norm graph and move it left/right and the yellow cursor on the L-curve will follow. At the same time you'll see the regularized distance distribution corresponding to that point as well as the back calculated dipolar data. The process can be interrupted by pressing the <esc> key. After creating the L-curve, you typically want to set the regularization as high as possible, but below the point where the residual norm increases significantly. The regularization parameter at the current cursor position is shown and can be applied to the setting on the fitting or Tikhonov tab by pressing [Apply].

Many criteria have been propose to determine the "best" regularization parameter (See here for example), but typically the optimum is relatively flat and the outcome is insensitive over a range near the optimal value. While other criteria will probably be implemented in the future, the current program uses a very simple algorithm to find an initial estimate: The L-curve is rotated in the complex plane and the minimum selected. When experimental features* are enabled, the rotation angle can be modified by the user. After the cursor has been moved around manually, pressing [Find again] will return the value to the position according to the above criteria.

In the presence of significant noise in the data the user is encouraged to manually find a reasonable compromise by watching the the distance distribution as the green cursor is moved left and right. Try to find the position where excessive spikes disappear, but before the distance peaks start to broaden significantly.

*To enable experimental features, go to the "Settings" tab and check the box.