Getting fitting goals (9) to work correctly requires a good
handle on several elements that are not necessarily easy
or even possible to achieve.
To demonstrate these problems, I am going to set up
a simple deblurring inversion problem.
The left panel of Figure shows the model that
we are going to attempt to invert for. The right panel of
Figure shows the data , the model blurred by a
simple known filter.
If we add random noise to the problem (left panel of Figure ),
we can quickly get an unreasonable model estimate (right
panel of Figure ).
If we add an isotropic regularizer, our estimate
improves substantially (Figure ).
We will speed up the
conversion of our problem
by preconditioning the problem with a symmetric
operator and start with
as our fitting goals.
Figure 3 The left panel is the model that we are going to attempt
to invert for. The right panel is the data, a blurred version
of the model.
The left panel is the data with Gaussian random noise added.
The right panel is the resulting model estimate.
Figure 5 The model estimated from the data shown in the left
panel of Figure using an isotropic regularization operator.