Shrinkage versus deconvolution

Inverse Problems

Volumn 23, Issue 5, 2007, Pages 2231-2248

  Klann, E ^a   Kuhn, M ^b   Lorenz, D A ^c   Maass, P ^c   Thiele, H ^b  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

^b BRUKER DALTONIK GMBH   (Germany)

^c UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR ALGEBRA; MATHEMATICAL MODELS; PROBLEM SOLVING; SHRINKAGE; WAVELET ANALYSIS;

BESOV SPACES; LINEAR REGULARIZATION; PEAK-LIKE STRUCTURES; WAVELET SHRINKAGE;

DECONVOLUTION;

EID: 37549026304     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/5/025     Document Type: Article

References (22)

1. Bredies K and Lorenz D A 2007 Iterated hard shrinkage for minimization problems with sparsity constraints SIAM J. Sci. Comput. at press
2. Bredies K, Lorenz D A and Maass P 2008 A generalized conditional gradient method and its connection to an iterative shrinkage method Comput. Optim. Appl. at press
3. Breiman L 1992 Probability (Philadelphia, PA: SIAM)
4. Brown J C 1995 Inverse problems in astrophysical spectrometry Inverse Problems 11 783-94
5. Brown J C 1995 Overview of topical issue on inverse problems in astronomy Inverse Problems 11 635-8
6. Candès E J 2006 Compressive sampling ed Sanz-Solé Marta et al ICM: Proc. Int. Congress of Mathematicians (Madrid, Spain, 22-30 Aug. 2006 vol 3 (Invited Lectures)) (Zürich: European Mathematical Society (EMS))
7. Candès E J, Romberg J K and Tao T 2005 Stable signal recovery from incomplete and inaccurate measurements Commun. Pure Appl. Math. 59 1207-23
8. Chan T F and Shen J J 2005 Image Processing and Analysis. Variational, PDE, Wavelet, and Stochastic Methods (Philadelphia, PA: SIAM)
9. Cohen A 2000 Wavelet methods in numerical analysis Handbook of Numerical Analysis Solution of Equations in Part 3. (Techniques of Scientific Computing vol 7) ed P G Ciarlet et al (Amsterdam: North-Holland/Elsevier) pp 417-711
10. Cohen A, DeVore R, Kerkyacharian G and Picard D 2001 Maximal spaces with given rate of convergence for thresholding algorithms Appl. Comput. Harmon. Anal. 11 167-91
11. Cohen A, Hoffmann M and Reiss M 2004 Adaptive wavelet Galerkin methods for linear inverse problems SIAM J. Numer. Anal. 42
12. Daubechies I, Defrise M and DeMol C 2004 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Commun. Pure Appl. Math. 57 1413-57
13. Dicken V and Maass P 1996 Wavelet-Galerkin methods for ill-posed problems J. Inverse Ill-Posed Problems 4 203-21
14. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Mathematics and its Applications (Dordrecht) vol 375) vol 8 (Dordrecht: Kluwer) p 321
15. Hanke M and Nagy J G 1996 Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques Inverse Problems 12 157-73
16. Hegland M and Anderssen R S 2005 Resolution enhancement of spectra using differentiation Inverse Problems 21 915-34
17. Justen L and Ramlau R 2006 A non-iterative regularization approach to blind deconvolution Inverse Problems 22 771-800
18. Klann E, Maass P and Ramlau R 2006 Two-step regularization methods for linear inverse problems Journal Inverse and Ill-Posed Problems 14 583-607
19. Lindemann M, Diaz M, Maass P, Schleif F-M, Decker J, Elssner T, Kuhn M and Thiele H 2006 Wavelet based feature extraction in the analysis of clinical proteomics mass spectra 54th Conference of the American Society for Mass Spectrometry
20. Mallat S 1998 A Wavelet Tour of Signal Processing vol 24 (San Diego, CA: Academic) p 577
21. Prünte L, Maass P and Thielemann H 2006 Condition monitoring of linear guide ways using a matched wavelet approach (submitted)
22. Ramlau R and Teschke G 2005 Tikhonov replacement functionals for iteratively solving nonlinear operator equations Inverse Problems 21 1571-92