abstract:
Regularization methods for linear ill-posed problems $ Kf = g $ have been extensively investigated when there exists noisy measurements $g^{\delta}$ for the true data $g$. However, often also the operator is not known exactly. A common way to solve this problem is to use the regularized total least squares method.
In our approach, we consider linear integral equations where we assume that both the kernel and the data are contaminated with noise, and use Tikhonov regularization for a stable reconstruction of both the kernel and the solution.
Finally, we discuss computational aspects and develop an iterative shrinkage-thresholding algorithm for the reconstruction, and provide first numerical results. |