Discrepancy Principle for Statistical Inverse Problems with Application to Conjugate Gradient Iteration
## AbstractThe authors discuss the use of the discrepancy principle for statis- tical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well-dened, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modi- cation of the discrepancy is introduced, which takes into account both of the above deciencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.
[Edit] |