Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers

We present a projection based regularization parameter choice approach within the framework of the linear sampling method for the reconstruction of acoustically penetrable objects. Using the Golub–Kahan bidiagonalization algorithm and the Lanczos tridiagonalization process we form appropriate subspaces which generate a sequence of regularized solutions. As a result two new and efficient methods are developed and used for the solution of problems that involve large linear systems of equations. The effectiveness of our approach is illustrated with reconstructions of three dimensional objects.