Matrix computations (3rd ed.)
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
Smoothing-Norm Preconditioning for Regularizing Minimum-Residual Methods
SIAM Journal on Matrix Analysis and Applications
Discrete Inverse Problems: Insight and Algorithms
Discrete Inverse Problems: Insight and Algorithms
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We focus on the solution of discrete ill-posed problems to recover the original information from blurred signals in the presence of Gaussian white noise more accurately. We derive seminorms for the Tikhonov---Phillips regularization based on the underlying blur operator H. In this way it is possible to improve the reconstruction using spectral information of H. Reconstructions on various 1D discrete ill-posed inverse problems demonstrate the effect of the presented approach.