The problem is reduced to the restoration of the unknown function,, or space distribution of the parameter, x, under test or the reconstruction of the object's image after the inversion of the operator type equation f(y) = A (x). Here f(y) is the set of experimental data and A - is the operator, which acts on the unknown function (x). This inversion is based upon a priority knowledge account while either minimizing (linear regularization) or maximizing (nonlinear Bayes regularization) some functionals.

In this report some new approaches to these procedures are considered, being applied to: (I) the restoration of stress distribution with depth resolution by Barkhausen noise (BN) technique, (ii) the restoration of layer by layer distribution of residual magnetization (and depended material's parameters) after the local magnetization by pick up coil, (iii) the restoration of the principal stress tensor components after BN measurements while tangential applied magnetic field is rotated, (iv) 3-D X- ray reconstruction of the flaws' images using limited views and projections (this is only the illustration of the results, which were received together with Dr. G. R. Tillack and Dr. K. Nockeman from German Federal Institute of Material Research and Testing).

Some new effective techniques for a priori knowledge insertion in the algorithms are considered. That is:

• using the support of the boundary conditions, Moore rule for plain stresses, demagnetizing conditions, etc.
• "education" of the solution, (c) support of some general geometrical features of the image.

The potentialities of various procedures and forms of a priori knowledge account in NDE inverse problems are evaluated.

Some results of the first International Conference on "Computer methods and inverse problems in Nondestructive testing and diagnostics" (CM NDT-95) held in Minsk in November 1995 are as well discussed.