  We study the influence of analytical regularization used in the generalized
function (distribution) space to the Tikhonov regularization procedure utilized
in the different versions of Moore-Penrose's inversion. By introducing a new
analytical term to the Tikhonov regularization of Moore-Penrose's inversion
procedure, we derive new optimization conditions that extend the Tikhonov
regularization framework and influence the fitting parameter. This enhancement
yields a more robust and accurate reconstruction of physical quantities,
demonstrating its potential impact on various studies. We illustrate the
significance of new term through schematic examples of physical applications,
highlighting its relevance to diverse fields. Our findings provide a valuable
tool for improving inversion methods and their applications in physics and
beyond.
