Abstract
There is a Poisson inverse problem in biomedical imaging, fluorescence microscopy and so on. Since the observed measurements are damaged by a linear operator and further destroyed by Poisson noise, recovering the 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 restore the observed image. In the network, the Conv-layers play the role of a linear inverse filter and the distribution transformation simultaneously. Furthermore, there is no batch normalization (BN) layer in the residual block of the network, which is devoted to tackling with the non-Gaussian recovery procedure. The proposed method is compared with state-of-the-art Poisson deblurring algorithms, and the experimental results show the effectiveness of the method.
Similar content being viewed by others
References
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.
DABOV K, FOI A, KATKOVNIK V, et al. Image restoration by sparse 3D transform-domain collaborative filtering [J]. Proceedings of SPIE, 2008, 6812: 681207.
XUE F, LUISIER F, BLU T. Multi-wiener SURE-LET deconvolution [J]. IEEE Transactions on Image Processing, 2013, 22(5): 1954–1968.
FIGUEIREDO M A T, BIOUCAS-DIAS J M. Restoration of Poissonian images using alternating direction optimization [J]. IEEE transactions on Image Processing, 2010, 19(12): 3133–3145.
LEFKIMMIATIS S, UNSER M. Poisson image reconstruction with Hessian Schatten-norm regularization [J]. IEEE Transactions on Image Processing, 2013, 22(11): 4314–4327.
SARDER P, NEHORAI A. Deconvolution methods for 3-D fluorescence microscopy images [J]. IEEE Signal Processing Magazine, 2006, 23(3): 32–45.
BERTERO M, BOCCACCI P, DESIDERÈ G, et al. Image deblurring with Poisson data: From cells to galaxies [J]. Inverse Problems, 2009, 25(12): 123006.
DEY N, BLANC-FERAUD L, ZIMMER C, et al. Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution [J]. Microscopy Research and Technique, 2006, 69(4): 260–266.
HARMANY Z T, MARCIA R F, WILLETT R M. This is SPIRAL-TAP: Sparse Poisson intensity reconstruction algorithms-theory and practice [J]. IEEE Transactions on Image Processing, 2011, 21(3): 1084–1096.
BENFENATI A, RUGGIERO V. Inexact Bregman iteration with an application to Poisson data reconstruction [J]. Inverse Problems, 2013, 29(6): 065016.
STARCK J L, MURTAGH F. Image restoration with noise suppression using the wavelet transform [J]. Astronomy and Astrophysics, 1994, 288: 342–348.
ANTONIADIS A, BIGOT J. Poisson inverse problems [J]. The Annals of Statistics, 2006, 34(5): 2132–2158.
CARLAVAN M, BLANC-FERAUD L. Sparse Poisson noisy image deblurring [J]. IEEE Transactions on Image Processing, 2011, 21(4): 1834–1846.
SETZER S, STEIDL G, TEUBER T. Deblurring Poissonian images by split Bregman techniques [J]. Journal of Visual Communication and Image Representation, 2010, 21(3): 193–199.
PUSTELNIK N, CHAUX C, PESQUET J C. Parallel proximal algorithm for image restoration using hybrid regularization — Extended version [J]. IEEE Transactions on Image Processing, 2011, 20(9): 2450–2462.
CHEN D Q. Regularized generalized inverse accelerating linearized alternating minimization algorithm for frame-based Poissonian image deblurring [J]. SIAM Journal on Imaging Sciences, 2014, 7: 716–739.
MA L Y, MOISAN L, YU J, et al. A dictionary learning approach for Poisson image deblurring [J]. IEEE Transactions on Medical Imaging, 2013, 32(7): 1277–1289.
DUPÉ F X, FADILI M J, STARCK J L. A proximal iteration for deconvolving Poisson noisy images using sparse representations [J]. IEEE Transactions on Image Processing, 2009, 18(2): 310–321.
AZZARI L, FOI A. Variance stabilization in Poisson image deblurring [C]//2017 IEEE 14th International Symposium on Biomedical Imaging. Melbourne, VIC: IEEE, 2017, 728–731.
ROND A, GIRYES R, ELAD M. Poisson inverse problems by the plug-and-play scheme [J]. Journal of Visual Communication and Image Representation, 2016, 41: 96–108.
KOLACZYK E D. Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds [J]. Statistica Sinica, 1999, 9: 119–135.
NOWAK R D, BARANIUK R G. Wavelet-domain filtering for photon imaging systems [J]. IEEE Transactions on Image Processing, 1999, 8(5): 666–678.
CHARLES C, RASSON J P. Wavelet denoising of Poisson-distributed data and applications [J]. Computational statistics & Data Analysis, 2003, 43: 139–148.
YANG S J, LEE B U. Poisson-Gaussian noise reduction using the hidden Markov model in contourlet domain for fluorescence microscopy images [J]. PLoS ONE, 2015, 10(9): e0136964.
ZHANG M H, ZHANG F Q, LIU Q G, et al. VST-Net: Variance-stabilizing transformation inspired network for Poisson denoising [J]. Journal of Visual Communication and Image Representation, 2019, 62: 12–22.
ANSCOMBE F J. The transformation of Poisson, binomial and negative-binomial data [J]. Biometrika, 1948, 35(3/4): 246–254.
DONOHO D L. Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data [C]//Proceedings of Symposia in Applied Mathematics. Providence: American Mathematical Society, 1993, 47: 173–205.
MÄKITALO M, FOI A. Optimal inversion of the Anscombe transformation in low-count Poisson image denoising [J]. IEEE Transactions on Image Processing, 2011, 20(1): 99–109.
FRYZLEWICZ P, NASON G P. A Haar-Fisz algorithm for Poisson intensity estimation [J]. Journal of Computational and Graphical Statistics, 2004, 13(3): 621–638.
ZHANG B, FADILI J M, STARCK J L. Wavelets ridgelets and curvelets for Poisson noise removal [J]. IEEE Transactions on Image Processing, 2008, 17(7): 1093–1108.
AZZARI L, FOI A. Variance stabilization for noisy+estimate combination in iterative Poisson denoising [J]. IEEE Signal Processing Letters, 2016, 23(8): 1086–1090.
WILLETT R. Multiscale analysis of photon-limited astronomical images [J]. Statistical Challenges in Modern Astronomy IV, 2007, 371: 247–264.
WU Z L, GAO H X, MA G, et al. A dual adaptive regularization method to remove mixed Gaussian-Poisson noise [J]. Lecture Notes in Computer Science, 2016, 10116: 206–221.
HE K M, ZHANG X Y, REN S Q, et al. Deep residual learning for image recognition [C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Las Vegas: IEEE, 2016, 770–778.
ZHANG K, ZUO W M, CHEN Y J, et al. Beyond a gaussian denoiser: Residual learning of deep CNN for image denoising [J]. IEEE Transactions on Image Processing, 2017, 26(7): 3142–3155.
LIU P, FANG R G. Learning pixel-distribution prior with wider convolution for image denoising [EB/OL]. [2020-01-30]. https://arxiv.org/pdf/1707.09135.pdf.
KIM J, LEE J K, LEE K M. Accurate image superresolution using very deep convolutional networks [C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Las Vegas: IEEE, 2016, 1646–1654.
LI J Z, LUISIER F, BLU T. Deconvolution of Poissonian images with the PURE-LET approach [C]//Proceedings of the 23rd IEEE International Conference on Image Processing (ICIP). Phoenix, Arizona: IEEE, 2016, 2708–2712.
LEFKIMMIATIS S, UNSER M. Poisson image reconstruction with Hessian Schatten-norm regularization [J]. IEEE Transactions on Image Processing, 2013, 22(11): 4314–4327.
WANG N N, SHI W X, FAN C E, et al. An improved nonlocal sparse regularization-based image deblurring via novel similarity criteria [J]. International Journal of Advanced Robotic Systems, 2018, 15(3): 1729881418783119.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: the National Natural Science Foundation of China (No. 61661031)
Rights and permissions
About this article
Cite this article
Xu, X., Zheng, H., Zhang, F. et al. Poisson Image Restoration via Transformed Network. J. Shanghai Jiaotong Univ. (Sci.) 26, 857–868 (2021). https://doi.org/10.1007/s12204-020-2235-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12204-020-2235-7
Key words
- deconvolution
- Poisson noise
- transformed network
- decouple scheme
- variance-stabilizing transformation (VST)