This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider so-called oversmoothing state sense that penalization is not able to capture true solution regularity and leads infinite penalty value solution. We establish vast extension of Hilbertian convergence through use invertible sectorial operators from h...

One of the essential ways in which nonlinear image restoration algorithms differ from linear, convolution-type image restoration filters is their capability to restrict the restoration result to nonnegative intensities. The iterative constrained Tikhonov-Miller (ICTM) algorithm, for example, incorporates the nonnegativity constraint by clipping all negative values to zero after each iteration. ...

Reconstructing a 3D face shape from a limited number of 2D facial feature points is considered as an ill-posed problem which can be solved using regularization. Tikhonov regularization is a popular method that incorporates prior information towards providing the existence of closed-form solutions which we obtain as a result of applying PCA, in order to solve the ill-posed problem. The common fa...

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification: 65F22, 65H05, 65R32.

Tikhonov regularization approach and block motion model are used to solve super-resolution problem for face video data. Video is preprocessed by 2-D empirical mode decomposition method to suppress illumination artifacts for super-resolution.

Received () Revised () We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.