On regularization of ill-posed problem using wavelets

The search of wavelet subspace (scale) in which the ill-posed problem is stable is considered. For every scale, the minimum eigenvalue of Hessian is calculated and compared with data error. This eigenvalue is calculated by iterations using the Hessian action by a vector. The residual gradient used for Hessian action is obtained via adjoint problem. The estimation of inflow parameters from outflow data for supersonic viscous flow was used as a model problem. The numerical tests demonstrate the feasibility of the stable scale estimation.