×

Bayesian smoothing of photon-limited images with applications in astronomy. (English) Zbl 1226.62025

Summary: We consider a multiscale model for intensities in photon-limited images using a Bayesian framework. A typical Dirichlet prior on relative intensities is not efficient in picking up structures owing to the continuity of intensities. We propose a novel prior using the so-called ‘Chinese restaurant process’ to create structures in the form of equal intensities of some neighbouring pixels. Simulations are conducted using several photon-limited images, which are common in X-ray astronomy and other high energy photon-based images. Applications to astronomical images from the Chandra X-ray Observatory satellite are shown. The new methodology outperforms most existing methods in terms of image processing quality, speed and the ability to select smoothing parameters automatically.

MSC:

62F15 Bayesian inference
85A35 Statistical astronomy
62H35 Image analysis in multivariate analysis
62M40 Random fields; image analysis
62P35 Applications of statistics to physics
65C60 Computational problems in statistics (MSC2010)

References:

[1] Baddeley, An error metric for binary images, Robust Computer Vision: Quality of Vision Algorithms pp 59– (1992)
[2] Coifman , R. R. Donoho , D. L. 1995 Wavelets and Statistics A. Antoniadis G. Oppenheim 125 150 Springer
[3] Donoho, Wedgelets: nearly minimax estimates of edges, Ann. Statist. 27 pp 859– (1999) · Zbl 0957.62029 · doi:10.1214/aos/1018031261
[4] Esch, An image restoration technique with error estimates, Astrophys. J. 610 pp 1213– (2004) · doi:10.1086/421761
[5] Ferguson, A Bayesian analysis of some nonparametric problems, Ann. Statist. 1 pp 209– (1973) · Zbl 0255.62037 · doi:10.1214/aos/1176342360
[6] Gull, Image reconstruction from incomplete and noisy data, Nature 272 pp 686– (1978) · doi:10.1038/272686a0
[7] Kolaczyk, Nonparametric estmation of gamma-ray burst intensities using Haar wavelets, Astrophys. J. 483 pp 340– (1997) · doi:10.1086/304243
[8] Kolaczyk, Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds, Statist. Sin. 9 pp 119– (1998) · Zbl 0927.62081
[9] Kolaczyk, Bayesian multiscale models for Poisson processes, J. Am. Statist. Ass. 94 pp 920– (1999) · Zbl 1072.62630 · doi:10.2307/2670007
[10] Kolaczyk, Multiscale likelihood analysis and complexity penalized estimation, Ann. Statist. 32 pp 500– (2004) · Zbl 1048.62036 · doi:10.1214/009053604000000076
[11] Nowak, A statistical multiscale framework for Poisson inverse problems, IEEE Trans. Inform. Theor. 46 pp 1811– (2000) · Zbl 0999.94004 · doi:10.1109/18.857793
[12] Pitman, Exchangeable and partially exchangeable random partitions, Probab. Theor. Reltd Flds 102 pp 145– (1995) · Zbl 0821.60047 · doi:10.1007/BF01213386
[13] Reynolds, The youngest galactic supernova remnant: G1.9+0.3, Astrophys. J. 680 pp 41– (2008) · doi:10.1086/589570
[14] Schwartz, On Bayes procedures, Z. Wahrsch. Ver. Geb. 4 pp 10– (1965) · Zbl 0158.17606 · doi:10.1007/BF00535479
[15] Schwarz, Estimating the dimension of a model, Ann. Statist. 6 pp 461– (1978) · Zbl 0379.62005 · doi:10.1214/aos/1176344136
[16] Starck, Astronomical Image and Data Analysis (2006) · doi:10.1007/978-3-540-33025-7
[17] Teh, Hierarchical Dirichlet processes, J. Am. Statist. Ass. 101 pp 1566– (2006) · Zbl 1171.62349 · doi:10.1198/016214506000000302
[18] Trumper, The Universe in X-rays (2008) · Zbl 1141.53063 · doi:10.1007/978-3-540-34412-4
[19] Willett, Multiscale analysis of photon-limited astronomical images, 4th Conf. Statistical Challenges in Modern Astronomy, State College, June 12th-15th (2006)
[20] Willett, Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging, IEEE Trans. Med. Imgng 22 pp 332– (2003) · doi:10.1109/TMI.2003.809622
[21] Willett, Proc. Int. Symp. Biomedical Imaging, Arlington, Apr. 15th-18th (2004)
[22] Wilson, A new metric for grey-scale image comparison, Int. J. Comput. Visn 24 pp 5– (1997) · doi:10.1023/A:1007978107063
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.