Research Article | Open | Published:
Iterative Desensitisation of Image Restoration Filters under Wrong PSF and Noise Estimates
EURASIP Journal on Advances in Signal Processingvolume 2007, Article number: 072658 (2007)
The restoration achieved on the basis of a Wiener scheme is an optimum since the restoration filter is the outcome of a minimisation process. Moreover, the Wiener restoration approach requires the estimation of some parameters related to the original image and the noise, as well as knowledge about the PSF function. However, in a real restoration problem, we may not possess accurate values of these parameters, making results relatively far from the desired optimum. Indeed, a desensitisation process is required to decrease this dependency on the parameter errors of the restoration filter. In this paper, we present an iterative method to reduce the sensitivity of a general restoration scheme (but specified to the Wiener filter) with regards to wrong estimates of the said parameters. Within the Fourier transform domain, a sensitivity analysis is tackled in depth with the purpose of defining a number of iterations for each frequency element, which leads to the aimed desensitisation regardless of the errors on estimates. Experimental computations using meaningful values of parameters are addressed. The proposed technique effectively achieves better results than those obtained when using the same wrong estimates in the Wiener approach, as well as verified on an SAR restoration.
Andrews HC, Hunt BR: Digital Image Restoration. Prentice-Hall, Englewood Cliffs, NJ, USA; 1977.
Gonzalez RC, Wintz P: Digital Image Processing. Addison Wesley, Reading, Mass, USA; 1992.
Tikhonov N, Arsenin VY: Solutions of Ill-Posed Problems, Scripta Series in Mathematics. John Wiley & Sons, New York, NY, USA; 1977.
Banham MR, Katsaggelos AK: Digital image restoration. IEEE Signal Processing Magazine 1997,14(2):24-41. 10.1109/79.581363
Lagendijk RL, Tekalp AM, Biemond JM: Maximum likelihood image and blur identification: a unifying approach. Optical Engineering 1990,29(5):422-435. 10.1117/12.55611
Reeves SJ, Mersereau RM: Blur identification by the method of generalized cross-validation. IEEE Transactions on Image Processing 1992,1(3):301–311. 10.1109/83.148604
Tekalp AM, Kaufman H, Woods JW: Identification of image and blur parameters for the restoration of noncausal blurs. IEEE Transactions on Acoustics, Speech, and Signal Processing 1986,34(4):963-972. 10.1109/TASSP.1986.1164886
You Y-L, Kaveh M: A regularization approach to joint blur identification and image restoration. IEEE Transactions on Image Processing 1996,5(3):416-428. 10.1109/83.491316
Giannakis GB, Heath RW Jr.: Blind identification of multichannel FIR blurs and perfect image restoration. IEEE Transactions on Image Processing 2000,9(11):1877-1896. 10.1109/83.877210
Feng C, Ma J-W, Chen J-P: The PSF correction method for satellite image restoration. Proceedings of the 3rd International Conference on Image and Graphics, December 2004, Hong Kong 31–34.
Ciftci M, Williams DB: Optimal estimation and sequential channel equalization algorithms for chaotic communications systems. EURASIP Journal on Applied Signal Processing 2001,2001(4):249-256. 10.1155/S1110865701000282
Galleani L, Cohen L, Nelson D, Scargle JD: Instantaneous spectrum estimation from event-based densities. EURASIP Journal on Applied Signal Processing 2002,2002(1):87-91. 10.1155/S1110865702000380
Hayenga M, Swan S, Zaharias A: Point Spread Function Estimation for the purpose of Motion Blurred Image Enhancement. 2002.
Devcic Z, Loncaric S: Blur identification using averaged spectra of degraded image singular vectors. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 4: 2195–2198.
Molina R, Katsaggelos AK, Mateos J, Hermoso A, Segall CA: Restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound Gauss-Markov random fields. Pattern Recognition 2000,33(4):555-571. 10.1016/S0031-3203(99)00072-2
Balram N, Moura JMF: Noncausal Gauss-Markov random fields: parameter structure and estimation. IEEE Transactions on Information Theory 1993,39(4):1333-1355. 10.1109/18.243450
Jeng FC, Woods JW: Compound Gauss-Markov models for image processing. In Digital Image Restoration, Springer Series in Information Science. Volume 23. Edited by: Katsaggelos AK. Springer, Berlin, Germany; 1991.
Martin-Fernandez M, San Josa-Estepar R, Westin C-F, Alberola-Lopez C: A novel Gauss-Markov random field approach for regularization of diffusion tensor maps. 9th International Conference on Computer Aided Systems Theory (EUROCAST '03), February 2003, Las Palmas de Gran Canaria, Spain, Lecture Notes in Computer Science 2809: 506–517.
Romberg JK, Choi H, Baraniuk RG: Bayesian tree-structured image modeling using wavelet-domain hidden Markov models. IEEE Transactions on Image Processing 2001,10(7):1056-1068. 10.1109/83.931100
Choi H, Baraniuk RG: Wavelet statistical models and Besov spaces. Wavelet Applications in Signal and Image Processing VII, July 1999, Denver, Colo, USA, Proceedings of SPIE 3813: 489–501.
Mallat SG: Multifrequency channel decompositions of images and wavelet models. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(12):2091-2110. 10.1109/29.45554
Koivunen V: A robust nonlinear filter for image restoration. IEEE Transactions on Image Processing 1995,4(5):569-578. 10.1109/83.382492
Voloshynovskiy S: Robust image restoration based on concept of M-estimation and parametric model of image spectrum. Proceedings of the 5th International Workshop on Systems, Signals and Image Processing (IWSSIP '98), June 1998, Zagreb, Croatia 123–126.
Allende H, Galbiati J, Vallejos R: Digital image restoration using autoregressive time series type models. Anais IX Simp'sio Brasileiro de Sensoriamento Remoto, September 1998, Santos, Brasil 1017–1027.
Hillery AD, Chin RT: Iterative Wiener filters for image restoration. IEEE Transactions on Signal Processing 1991,39(8):1892-1899. 10.1109/78.91161
Lagendijk RL, Biemond J, Boekee DE: Regularized iterative image restoration with ringing reduction. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988,36(12):1874-1888. 10.1109/29.9032
Nagy JG, Plemmons RJ, Torgersen TC: Iterative image restoration using approximate inverse preconditioning. IEEE Transactions on Image Processing 1996,5(7):1151-1162. 10.1109/83.502394
Erbas C, Kent S: A new iterative technique for image restoration of ERS-2 raw data. Proceedings of International Conference on Recent Advances in Space Technologies (RAST '03), November 2003, Istanbul, Turkey 85–90.
Haind M: Recursive model-based image restoration. Proceedings of the 15th International Conference on Pattern Recognition (ICPR '00), September 2000, Barcelona, Spain 3: 342–345.
Click SJ, Xia W: Iterative restoration of SPECT projection images. IEEE Transactions on Nuclear Science 1997,44(2):204-211. 10.1109/23.568807
Moon JI, Kim SK, Paik JK, Kang MG: Fast iterative image restoration algorithms. Proceedings of IEEE Asia Pacific Conference on Circuits and Systems, November 1996, Seoul, Korea 361–364.
Noonan JP, Natarajan P: A general formulation for iterative restoration methods. IEEE Transactions on Signal Processing 1997,45(10):2590-2593. 10.1109/78.640726
Lee SH, Cho NI, Park J-I: Directional regularisation for constrained iterative image restoration. Electronics Letters 2003,39(23):1642-1643. 10.1049/el:20031064
Chen W, Chen M, Zhou J: Adaptively regularized constrained total least-squares image restoration. IEEE Transactions on Image Processing 2000,9(4):588-596. 10.1109/83.841936
Choy SO, Chan YH, Siu WC: Image restoration by regularisation in uncorrelated transform domain. IEE Proceedings: Vision, Image and Signal Processing 2000,147(6):587-594. 10.1049/ip-vis:20000383
Cisneros G, Bernués E, Rodríguez I, Santiago MA, Álvarez F: Desensitisation of medical images restoration under crude estimates of mobile radio channels. Proceedings of IEEE International Conference on Image Processing (ICIP '04), October 2004, Singapore 1: 315–319.
Molina R, Katsaggelos AK, Mateos J: Bayesian and regularization methods for hyperparameter estimation in image restoration. IEEE Transactions on Image Processing 1999,8(2):231-246. 10.1109/83.743857
Molina R, Mateos J, Katsaggelos AK: Blind deconvolution using a variational approach to parameter, image, and blur estimation. IEEE Transactions on Image Processing 2006,15(12):3715-3727.
Corless RM, Gonnet GH, Hare DEG, Jeffrey DJ, Knuth DE: On the Lambert W function. Advances in Computational Mathematics 1996,5(4):329-359.