Discussion

The preceding section derives the relationship between the filtering and subtraction methods. The preconditioning changes the nature of the problem quite deeply: from a filtering algorithm we end-up with a prediction/subtraction method. The least-squares inverses in equations (3) and () are also very different: from a problem with one unknown, ${\bf s}$, we end-up with a problem with two unknowns, ${\bf m_n}$ and ${\bf m_s}$. Fortunately, this preconditioning should speed-up the convergence toward the signal vector ${\bf s}$.In addition, this transformation separates the data space in its natural components, e.g, the signal and noise vectors more explicitely than with the filtering method.