Reconstructing ionospheric electron density (IED) is an ill-posed inverse problem, with classical Tikhonov regularization tending to smooth IED structures. By contrast, total variation (TV) regularization effectively resists noise and preserves discontinuities of the IED. In this paper, we regularize the inverse problem by incorporating both Tikhonov and TV regularization. A specific formulatio...

Modern imaging technologies have been at the forefront of scientific research and medical diagnosis. Typically, the cost of producing these images is quite high, while device defects, environmental variations, as well as movements generated by the objects being imaged, may result in noisy, poor-quality images. As a method to improve the cost-benefit of imaging technologies, image deblurring has...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...