MetaCartSign in to MyCiteSeer

Include Citations | Advanced Search | Help

Include Citations | Advanced Search | Help

  Analysis of bounded variation penalty methods for ill-posed problems (1994) [56 citations — 1 self]

Download:
Download as a PDF | Download as a PS
by R. Acar, C. R. Vogel
Inverse Problems
http://www.math.montana.edu/~vogel/Papers/tvanalysis.ps.gz
Add To MetaCart

Abstract:

Abstract. This paper presents an abstract analysis of bounded variation (BV) methods for ill-posed operator equations Au = z. Let T (u) def = kAu \Gamma zk 2 + ffJ(u); where the penalty, or "regularization", parameter ff? 0 and the functional J(u) is the BV norm or seminorm of u, also known as the total variation of u. Under mild restrictions on the operator A and the functional J(u), it is shown that the functional T (u) has a unique minimizer which is stable with respect to certain perturbations in the data z, the operator A, the parameter ff, and the functional J(u). In addition, convergence results are obtained which apply when these perturbations vanish and the regularization parameter is chosen appropriately.

Citations

513 Nonlinear total variation based noise removal algorithms – Rudin, Osher, et al. - 1992
141 Minimal Surfaces and Functions of Bounded Variation – Giusti - 1984
101 Nonlinear Functional Analysis – Deimling - 1985
20 Identification of discontinuous parameters in flow equations – Gutman - 1990
19 An image enhancement technique for electrical impedance tomography – Dobson, Santosa - 1994
17 Applications of Functional Analysis and Operator Theory – Hutson, Pym - 1980
9 Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems – Seidman, Vogel - 1989
4 Denoising and Deblurring Algorithms with Constrained Nonlinear PDE's, submitted to – Lions, Osher, et al.
4 Reconstruction of blocky impedance profiles from normal incidence reflection seismograms which are band-limited and miscalibrated – Santosa, Symes - 1988
2 Funzioni BV e tracce – Anzellotti, Giaquinta - 1978
2 Total Variation Based Restoration of Noisy – Rudin, Osher, et al.
2 Total Variation regularization for ill-posed problems – Vogel - 1993
View or Download | Add to My Collection | Correct Errors