A new interpretation of (Tikhonov) regularization

Abstract Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, results on convergence theory are based technical proofs and sometimes difficult to interpret. It is also often not clear how those translate into discrete, numerical setting. In this paper we present a new strategy study properties of method example regularization. The technique well-known observation that approximates unknown exact solution range adjoint operator. This closely related concept approximate source conditions, which generalize describe only approximation solution, but noise-free noisy data; all from same space. Combining these three derive concise way improve understanding by tightening relation between concepts such as rates, parameter choice, saturation. limited regularization, it can be applied iterative demonstrate relating Landweber iteration. All accompanied examples.