The L-curve method to select the best regularization parameter:
Run reconstruction for a sweep of regularization parameters. Compute the residual norm of each, and the penalty term value of each reconstruction. Plot (typically in loglog) the penality value vs the residual norm for all regularization parameters. This will often/sometimes take the shape of a capital "L". The best regularization parameter (in the L-curve sense) is selected as the value at the corner. This is the best trade-off between fitting the data and a small penalty.
The L-curve method to select the best regularization parameter: Run reconstruction for a sweep of regularization parameters. Compute the residual norm of each, and the penalty term value of each reconstruction. Plot (typically in loglog) the penality value vs the residual norm for all regularization parameters. This will often/sometimes take the shape of a capital "L". The best regularization parameter (in the L-curve sense) is selected as the value at the corner. This is the best trade-off between fitting the data and a small penalty.