Mean curvature regularization-based Poisson image restoration

Abstract. The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as medical imaging, microscopy imaging, and so on. We focus on mean curvature-based regularization to address the Poisson noise image restoration problem. Furthermore, we derive a numerical algorithm based on the augmented Lagrange multiplier method with a splitting technique. In order to simultaneously demonstrate the effectiveness of the proposed method for Poisson noise removal with deblurring, we conduct systematic experiments on both nature images and biological images. Experimental results show that the proposed approach can produce higher quality results and more natural images compared to some state-of-the-art variational algorithms recently developed.

[2]  P. Lions,et al.  Splitting Algorithms for the Sum of Two Nonlinear Operators , 1979 .

[3]  Xue-Cheng Tai,et al.  Augmented Lagrangian method for a mean curvature based image denoising model , 2013 .

[4]  Jean-Luc Starck,et al.  Multichannel Poisson denoising and deconvolution on the sphere: application to the Fermi Gamma-ray Space Telescope , 2012, 1206.2787.

[5]  Laure Blanc-Féraud,et al.  Sparse Poisson Noisy Image Deblurring , 2012, IEEE Transactions on Image Processing.

[6]  S. Gibson,et al.  Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[7]  Karen O. Egiazarian,et al.  Deblurring of Poissonian images using BM3D frames , 2011, Optical Engineering + Applications.

[8]  S. Gibson,et al.  Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy. , 1991, Journal of the Optical Society of America. A, Optics and image science.

[9]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[10]  Chuanjiang He,et al.  Fractional order total variation regularization for image super-resolution , 2013, Signal Process..

[11]  M Unser,et al.  3‐D PSF fitting for fluorescence microscopy: implementation and localization application , 2013, Journal of microscopy.

[12]  José M. Bioucas-Dias,et al.  An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems , 2009, IEEE Transactions on Image Processing.

[13]  Tony F. Chan,et al.  Image Denoising Using Mean Curvature of Image Surface , 2012, SIAM J. Imaging Sci..

[14]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[15]  Rob Fergus,et al.  Blind deconvolution using a normalized sparsity measure , 2011, CVPR 2011.

[16]  Michael Unser,et al.  3D Poisson microscopy deconvolution with Hessian Schatten-norm regularization , 2013, 2013 IEEE 10th International Symposium on Biomedical Imaging.

[17]  Thierry Blu,et al.  Fast interscale wavelet denoising of Poisson-corrupted images , 2010, Signal Process..

[18]  Mohamed-Jalal Fadili,et al.  A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations , 2008, IEEE Transactions on Image Processing.

[19]  Xiangchu Feng,et al.  Multiplicative noise removal via sparse and redundant representations over learned dictionaries and total variation , 2012, Signal Process..

[20]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[21]  Gabriele Steidl,et al.  Deblurring Poissonian images by split Bregman techniques , 2010, J. Vis. Commun. Image Represent..

[22]  Sylvain Paris,et al.  Handling Noise in Single Image Deblurring Using Directional Filters , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[23]  José M. Bioucas-Dias,et al.  An augmented Lagrangian approach to linear inverse problems with compound regularization , 2010, 2010 IEEE International Conference on Image Processing.

[24]  Guan Yu,et al.  Variance stabilizing transformations of Poisson, binomial and negative binomial distributions , 2009 .

[25]  Keigo Hirakawa,et al.  Blur Processing Using Double Discrete Wavelet Transform , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[26]  J. Aujol,et al.  Some proximal methods for Poisson intensity CBCT and PET , 2012 .

[27]  Karl Kunisch,et al.  Total Generalized Variation , 2010, SIAM J. Imaging Sci..

[28]  Binjie Qin,et al.  Reducing Poisson noise and baseline drift in x-ray spectral images with bootstrap Poisson regression and robust nonparametric regression , 2013, Physics in medicine and biology.

[29]  José M. Bioucas-Dias,et al.  Restoration of Poissonian Images Using Alternating Direction Optimization , 2010, IEEE Transactions on Image Processing.

[30]  Karen O. Egiazarian,et al.  BM3D Frames and Variational Image Deblurring , 2011, IEEE Transactions on Image Processing.

[31]  Søren Holdt Jensen,et al.  Algorithms and software for total variation image reconstruction via first-order methods , 2009, Numerical Algorithms.

[32]  Michael Unser,et al.  Poisson Image Reconstruction With Hessian Schatten-Norm Regularization , 2013, IEEE Transactions on Image Processing.

[33]  Xue-Cheng Tai,et al.  A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method , 2011, SIAM J. Imaging Sci..

[34]  Jian Yu,et al.  A Dictionary Learning Approach for Poisson Image Deblurring , 2013, IEEE Transactions on Medical Imaging.