×

zbMATH — the first resource for mathematics

Scaling techniques for gradient projection-type methods in astronomical image deblurring. (English) Zbl 1278.68326
Summary: The aim of this paper is to present a computational study on scaling techniques in gradient projection-type (GP-type) methods for deblurring of astronomical images corrupted by Poisson noise. In this case, the imaging problem is formulated as a non-negatively constrained minimization problem in which the objective function is the sum of a fit-to-data term, the Kullback-Leibler divergence, and a Tikhonov regularization term. The considered GP-type methods are formulated by a common iteration formula, where the scaling matrix and the step-length parameter characterize the different algorithms. Within this formulation, both first-order and Newton-like methods are analysed, with particular attention to those implementation features and behaviours relevant for the image restoration problem. The numerical experiments show that suited scaling strategies can enable the GP methods to quickly approximate accurate reconstructions and then are useful for designing effective image deblurring algorithms.

MSC:
68U10 Computing methodologies for image processing
65K05 Numerical mathematical programming methods
65F22 Ill-posedness and regularization problems in numerical linear algebra
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anscombe F. J., Biometrika 35 pp 246– (1940) · Zbl 0032.03702
[2] DOI: 10.1080/17415970701404235 · Zbl 1258.35206
[3] DOI: 10.1007/s10444-008-9081-8 · Zbl 1171.94001
[4] DOI: 10.1137/S1064827502410451 · Zbl 1061.65047
[5] DOI: 10.1093/imanum/8.1.141 · Zbl 0638.65055
[6] Benvenuto F., Inverse Problems 26 (2010) · Zbl 1375.65078
[7] DOI: 10.1887/0750304359
[8] Bertero M., CRM series 7, Edizioni della Normale, Pisa, in: Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy pp 37– (2008)
[9] DOI: 10.1088/0266-5611/25/12/123006 · Zbl 1186.85001
[10] DOI: 10.1088/0266-5611/27/11/113001 · Zbl 1252.85004
[11] DOI: 10.1137/0320018 · Zbl 0507.49018
[12] Bertsekas D., Nonlinear Programming, 2. ed. (2003) · Zbl 0935.90037
[13] DOI: 10.1093/imanum/23.4.539 · Zbl 1047.65042
[14] DOI: 10.1088/0266-5611/27/9/095001 · Zbl 1252.94008
[15] Bonettini S., J. Math. Imaging Vis. (2012)
[16] DOI: 10.1016/j.cam.2009.02.020 · Zbl 1167.94003
[17] DOI: 10.1088/0266-5611/25/1/015002 · Zbl 1155.94011
[18] DOI: 10.1111/j.1365-2966.2004.08524.x
[19] DOI: 10.1214/aos/1176348385 · Zbl 0753.62003
[20] DOI: 10.1007/s00211-004-0569-y · Zbl 1068.65073
[21] DOI: 10.1007/s10107-005-0595-2 · Zbl 1134.90030
[22] DOI: 10.1093/imanum/drl006 · Zbl 1147.65315
[23] DOI: 10.1109/TMI.1986.4307748
[24] DOI: 10.1109/TIP.2008.2008223 · Zbl 1371.94117
[25] DOI: 10.1109/TIP.2010.2053941 · Zbl 1371.94128
[26] DOI: 10.3934/jimo.2008.4.299 · Zbl 1161.90524
[27] DOI: 10.1137/0322061 · Zbl 0555.90086
[28] DOI: 10.1109/TPAMI.1984.4767596 · Zbl 0573.62030
[29] DOI: 10.1007/s10107-007-0199-0 · Zbl 1168.90007
[30] DOI: 10.1088/0266-5611/12/2/004 · Zbl 0859.65141
[31] Hansen P. C., Deblurring Images. Matrices, Spectra and Filtering (2006) · Zbl 1112.68127
[32] Landi G., Int. J. Math. Comput. Sci. 3 (3) pp 199– (2008)
[33] DOI: 10.1007/s11075-008-9198-3 · Zbl 1151.65053
[34] DOI: 10.1007/s11075-011-9517-y · Zbl 1241.65059
[35] DOI: 10.1016/j.compmedimag.2011.07.002
[36] DOI: 10.1088/0266-5611/18/5/313 · Zbl 1023.62099
[37] DOI: 10.1007/s10851-007-0652-y
[38] DOI: 10.1086/111605
[39] DOI: 10.1007/b98874 · Zbl 0930.65067
[40] DOI: 10.1364/JOSA.62.000055
[41] DOI: 10.1007/s10898-009-9516-x · Zbl 1202.90244
[42] DOI: 10.1109/TMI.1982.4307558
[43] DOI: 10.1137/1.9780898717570 · Zbl 1008.65103
[44] DOI: 10.1088/0266-5611/25/4/045010 · Zbl 1163.65042
[45] DOI: 10.1007/s10589-006-6446-0 · Zbl 1121.90099
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.