Poisson Image Restoration via Transformed Network

doi:10.1007/s12204-020-2235-7

摘要/Abstract

Abstract: There is a Poisson inverse problem in biomedical imaging, fluorescence microscopy and so on. Sincethe observed measurements are damaged by a linear operator and further destroyed by Poisson noise, recoveringthe approximate original image is difficult. Motivated by the decouple scheme and the variance-stabilizing transformation(VST) strategy, we propose a method of transformed convolutional neural network (CNN) to restorethe observed image. In the network, the Conv-layers play the role of a linear inverse filter and the distributiontransformation simultaneously. Furthermore, there is no batch normalization (BN) layer in the residual block ofthe network, which is devoted to tackling with the non-Gaussian recovery procedure. The proposed method iscompared with state-of-the-art Poisson deblurring algorithms, and the experimental results show the effectivenessof the method.

Key words: deconvolution, Poisson noise, transformed network, decouple scheme, variance-stabilizing transformation(VST)

中图分类号:

TP 751

. [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(6): 857-868.

XU Xiaoling (徐晓玲), ZHENG Haiyu (郑海玉), ZHANG Fengqin (张凤芹),LI Hechen (李赫辰), ZHANG Minghui∗ (张明辉). Poisson Image Restoration via Transformed Network[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(6): 857-868.

参考文献

[1] BARRETT H H. Objective assessment of image quality:Effects of quantum noise and object variability[J]. Journal of the Optical Society of America A, 1990,7(7): 1266-1278. [2] DABOV K, FOI A, KATKOVNIK V, et al. Imagerestoration by sparse 3D transform-domain collaborativefiltering [J]. Proceedings of SPIE, 2008, 6812:681207. [3] XUE F, LUISIER F, BLU T. Multi-wiener SURE-LETdeconvolution [J]. IEEE Transactions on Image Processing,2013, 22(5): 1954-1968. [4] FIGUEIREDOMA T, BIOUCAS-DIAS JM. Restorationof Poissonian images using alternating directionoptimization [J]. IEEE transactions on Image Processing,2010, 19(12): 3133-3145. [5] LEFKIMMIATIS S, UNSER M. Poisson image reconstructionwith Hessian Schatten-norm regularization[J]. IEEE Transactions on Image Processing, 2013,22(11): 4314-4327. [6] SARDER P, NEHORAI A. Deconvolution methods for3-D fluorescence microscopy images [J]. IEEE SignalProcessing Magazine, 2006, 23(3): 32-45. [7] BERTERO M, BOCCACCI P, DESIDER`A G, et al.Image deblurring with Poisson data: From cells togalaxies [J]. Inverse Problems, 2009, 25(12): 123006. [8] DEY N, BLANC-FERAUD L, ZIMMER C, et al.Richardson-Lucy algorithm with total variation regularizationfor 3D confocal microscope deconvolution[J]. Microscopy Research and Technique, 2006, 69(4):260-266. [9] HARMANY Z T,MARCIA R F, WILLETT RM. Thisis SPIRAL-TAP: Sparse Poisson intensity reconstructionalgorithms-theory and practice [J]. IEEE Transactionson Image Processing, 2011, 21(3): 1084-1096. [10] BENFENATI A, RUGGIERO V. Inexact Bregman iterationwith an application to Poisson data reconstruction[J]. Inverse Problems, 2013, 29(6): 065016. [11] STARCK J L, MURTAGH F. Image restoration withnoise suppression using the wavelet transform [J]. Astronomyand Astrophysics, 1994, 288: 342-348. [12] ANTONIADIS A, BIGOT J. Poisson inverse problems[J]. The Annals of Statistics, 2006, 34(5): 2132-2158. [13] CARLAVAN M, BLANC-F′ERAUD L. Sparse Poissonnoisy image deblurring [J]. IEEE Transactions on ImageProcessing, 2011, 21(4): 1834-1846. [14] SETZER S, STEIDL G, TEUBER T. Deblurring Poissonianimages by split Bregman techniques [J]. Journalof Visual Communication and Image Representation,2010, 21(3): 193-199. [15] PUSTELNIK N, CHAUX C, PESQUET J C. Parallelproximal algorithm for image restoration using hybridregularization – Extended version [J]. IEEE Transactionson Image Processing, 2011, 20(9): 2450-2462. [16] CHEN D Q. Regularized generalized inverse acceleratinglinearized alternating minimization algorithm forframe-based Poissonian image deblurring [J]. SIAMJournal on Imaging Sciences, 2014, 7: 716-739. [17] MA L Y, MOISAN L, YU J, et al. A dictionary learningapproach for Poisson image deblurring [J]. IEEETransactions on Medical Imaging, 2013, 32(7): 1277-1289. [18] DUP′E F X, FADILI M J, STARCK J L. A proximaliteration for deconvolving Poisson noisy images usingsparse representations [J]. IEEE Transactions on ImageProcessing, 2009, 18(2): 310-321. [19] AZZARI L, FOI A. Variance stabilization in Poissonimage deblurring [C]//2017 IEEE 14th InternationalSymposium on Biomedical Imaging. Melbourne, VIC:IEEE, 2017: 728-731. [20] ROND A, GIRYES R, ELAD M. Poisson inverse problemsby the plug-and-play scheme [J]. Journal of VisualCommunication and Image Representation, 2016,41: 96-108. [21] KOLACZYK E D.Wavelet shrinkage estimation of certainPoisson intensity signals using corrected thresholds[J]. Statistica Sinica, 1999, 9: 119-135. [22] NOWAK R D, BARANIUK R G. Wavelet-domain filteringfor photon imaging systems [J]. IEEE Transactionson Image Processing, 1999, 8(5): 666-678. [23] CHARLES C, RASSON J P. Wavelet denoising ofPoisson-distributed data and applications [J]. Computationalstatistics & Data Analysis, 2003, 43: 139-148. [24] YANG S J, LEE B U. Poisson-Gaussian noise reductionusing the hidden Markov model in contourletdomain for fluorescence microscopy images [J]. PLoSONE, 2015, 10(9): e0136964. [25] ZHANG M H, ZHANG F Q, LIU Q G, et al. VSTNet:Variance-stabilizing transformation inspired networkfor Poisson denoising [J]. Journal of Visual Communicationand Image Representation, 2019, 62: 12-22. [26] ANSCOMBE F J. The transformation of Poisson, binomialand negative-binomial data [J]. Biometrika,1948, 35(3/4): 246-254. [27] DONOHO D L. Nonlinear wavelet methods for recoveryof signals, densities, and spectra from indirect andnoisy data [C]//Proceedings of Symposia in AppliedMathematics. Providence: American Mathematical Society,1993, 47: 173-205. [28] M¨AKITALO M, FOI A. Optimal inversion of theAnscombe transformation in low-count Poisson imagedenoising [J]. IEEE Transactions on Image Processing,2011, 20(1): 99-109. [29] FRYZLEWICZ P, NASON G P. A Haar-Fisz algorithmfor Poisson intensity estimation [J]. Journal ofComputational and Graphical Statistics, 2004, 13(3):621-638. [30] ZHANG B, FADILI J M, STARCK J L. Waveletsridgelets and curvelets for Poisson noise removal [J].IEEE Transactions on Image Processing, 2008, 17(7):1093-1108. [31] AZZARI L, FOI A. Variance stabilization fornoisy+estimate combination in iterative Poisson denoising[J]. IEEE Signal Processing Letters, 2016,23(8): 1086-1090. [32] WILLETT R. Multiscale analysis of photon-limited astronomicalimages [J]. Statistical Challenges in ModernAstronomy IV, 2007, 371: 247-264. [33] WU Z L, GAO H X, MA G, et al. A dual adaptive regularizationmethod to remove mixed Gaussian-Poissonnoise [J]. Lecture Notes in Computer Science, 2016,10116: 206-221. [34] HE K M, ZHANG X Y, REN S Q, et al. Deep residuallearning for image recognition [C]//Proceedings ofthe IEEE Conference on Computer Vision and PatternRecognition. Las Vegas: IEEE, 2016: 770-778. [35] ZHANG K, ZUO W M, CHEN Y J, et al. Beyonda gaussian denoiser: Residual learning of deep CNNfor image denoising [J]. IEEE Transactions on ImageProcessing, 2017, 26(7): 3142-3155. [36] LIU P, FANG R G. Learning pixel-distribution priorwith wider convolution for image denoising [EB/OL].[2020-01-30]. https://arxiv.org/pdf/1707.09135.pdf. [37] KIM J, LEE J K, LEE K M. Accurate image superresolutionusing very deep convolutional networks[C]//Proceedings of the IEEE Conference on ComputerVision and Pattern Recognition. Las Vegas: IEEE,2016: 1646-1654. [38] LI J Z, LUISIER F, BLU T. Deconvolution of Poissonianimages with the PURE-LET approach [C]// Proceedingsof the 23rd IEEE International Conference onImage Processing (ICIP). Phoenix, Arizona: IEEE,2016: 2708-2712. [39] LEFKIMMIATIS S, UNSER M. Poisson image reconstructionwith Hessian Schatten-norm regularization[J]. IEEE Transactions on Image Processing, 2013,22(11): 4314-4327. [40] WANG N N, SHI W X, FAN C E, et al. An improvednonlocal sparse regularization-based image deblurringvia novel similarity criteria [J]. InternationalJournal of Advanced Robotic Systems, 2018, 15(3):1729881418783119.