Main Approaches to the Regularization of Ill‐posed Problems

[1]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.

[2]  J. B. Diaz,et al.  On iteration procedures for equations of the first kind, $Ax=y$, and Picard’s criterion for the existence of a solution , 1970 .

[3]  D. M. Titterington,et al.  A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  R. Mersereau,et al.  Optimal estimation of the regularization parameter and stabilizing functional for regularized image restoration , 1990 .

[5]  Guy Le Besnerais,et al.  A new look at entropy for solving linear inverse problems , 1999, IEEE Trans. Inf. Theory.

[6]  Fionn Murtagh,et al.  Deconvolution in Astronomy: A Review , 2002 .

[7]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[8]  Jane Cullum,et al.  The effective choice of the smoothing norm in regularization , 1979 .

[9]  P. Gilbert.  Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.

[10]  G. Wahba.  Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy , 1977 .

[11]  L. Landweber.  An iteration formula for Fredholm integral equations of the first kind , 1951 .

[12]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Ali Mohammad-Djafari,et al.  Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF , 1998, IEEE Trans. Image Process..

[14]  Guy Demoment,et al.  Minimization of strictly convex functions: an improved optimality test based on Fenchel duality , 2000 .

[15]  Horst Bialy.  Iterative behandlung linearer funktionalgleichungen , 1959 .

[16]  Ken D. Sauer,et al.  A generalized Gaussian image model for edge-preserving MAP estimation , 1993, IEEE Trans. Image Process..

[17]  Eric Walter,et al.  A general-purpose global optimizer: implementation and applications , 1984 .

[18]  D. Titterington.  Common structure of smoothing techniques in statistics , 1985 .

[19]  L. Lucy.  An iterative technique for the rectification of observed distributions , 1974 .

[20]  M. Sezan,et al.  Image Restoration by the Method of Convex Projections: Part 2-Applications and Numerical Results , 1982, IEEE Transactions on Medical Imaging.

[21]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[22]  Stéphane Mallat,et al.  Deconvolution by thresholding in mirror wavelet bases , 2003, IEEE Trans. Image Process..

[23]  M. Nashed.  Operator-theoretic and computational approaches to Ill-posed problems with applications to antenna theory , 1981 .

[24]  Gabor T. Herman,et al.  On the Bayesian Approach to Image Reconstruction , 1979, Inf. Control..

[25]  Ker-Chau Li,et al.  Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing , 1986 .

[26]  Yves Goussard,et al.  GCV and ML Methods of Determining Parameters in Image Restoration by Regularization: Fast Computation in the Spatial Domain and Experimental Comparison , 1993, J. Vis. Commun. Image Represent..

[27]  Donald Geman,et al.  Constrained Restoration and the Recovery of Discontinuities , 1992, IEEE Trans. Pattern Anal. Mach. Intell..