Regularization: the exact solution

The Exact Solution to the Geomagnetic Prospecting Problem

The left figure shows the exact solution. It is discontinuous.

The right figure shows the best PP-TSVD solution, which is obtained with the parameter k = 4.

The smooth TSVD solutions are poor approximations to this particular exact solution; but may be better than the PP-TSVD solutions for other ill-posed problems.

Conclusion: the solution depends strongly on the assumptions being made!