Errors of regularisation under range inclusions using variable Hilbert scales (Q645842)

Let \(X\) and \(Y\) be infinite-dimensional separable Hilbert spaces. The paper is concerned with linear ill-posed operator equations \(Af=g\), where the exact element \(g\) is given by an approximation \(g^{\delta}\), \(\| g-g^{\delta}\| \leq \delta\). Based on the variable Hilbert scale interpolation inequality, the authors derive bounds for the error of regularization methods under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators with non-closed range are given. Several examples from image processing and spectral enhancement illustrate how the new error bounds can be applied.