Image restoration is an important part of various applications, such as computer vision, robotics and
remote sensing. However, recovering the underlying structures of the latent image contained in multi-image is a
challenging problem because of the need to develop robust and fast algorithms. In this paper, a novel problem
formulation for multi-image restoration problem is proposed. This novel formulation is composed of multi-data
fidelity terms and a composite regularizer. The proposed regularizer consists of total generalized variation (TGV)
and lp-norm. This multi-regularization method can simultaneously exploit the consistence of image pixels and
promote the sparsity of natural signals. To deal with the resulting problem, we derive and implement the solution
using alternating direction method of multipliers (ADMM). The effectiveness of our method is illustrated through
extensive experiments on multi-image denoising and inpainting. Numerical results show that the proposed method
is more efficient than competing algorithms, achieving better restoration performance.
REN Xuanguang (任炫光), PAN Han (潘汉), JING Zhongliang (敬忠良), GAO Lei (高磊)
. Multi-Image Restoration Method Combined with Total Generalized Variation and lp-Norm Regularizations[J]. Journal of Shanghai Jiaotong University(Science), 2019
, 24(5)
: 551
-558
.
DOI: 10.1007/s12204-019-2113-3
[1] CAI J F, CHAN R H, NIKOLOVA M. Two-phase approach for deblurring images corrupted by impulse plus Gaussian noise [J]. Inverse Problems and Imaging,2008, 2(2): 187-204.
[2] BI S, HAN X G, YU Y Z. An L1 image transform for edge-preserving smoothing and scene-level intrinsic decomposition[J]. ACM Transactions on Graphics, 2015,34(4): 78.
[3] REN X G, PAN H, JING Z L, et al. Multi-images restoration method with a mixed-regularization approach for cognitive informatics [C]//International Conference on Cognitive Informatics & Cognitive Computing. Berkeley, CA: IEEE, 2018: 423-430.
[4] DONOHO D L, JOHNSTONE I M. Adapting to unknown smoothness via wavelet shrinkage [J]. Journal of the American Statistical Association, 1995, 90(432):1200-1224.
[5] YUE L W, SHEN H F, YUAN Q Q, et al. A locally adaptive L1-L2 norm for multi-frame super-resolution of images with mixed noise and outliers [J]. Signal Processing,2014, 105: 156-174.
[6] CETIN M, KARL W C. Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization [J]. IEEE Transactions on Image Processing,2001, 10(4): 623-631.
[7] CHARTRAND R. Exact reconstruction of sparse signals via nonconvex minimization [J]. IEEE Signal Processing Letters, 2007, 14(10): 707-710.
[8] BREDIES K, KUNISCH K, POCK T. Total generalized variation [J]. SIAM Journal on Imaging Sciences,2013, 3(3): 492-526.
[9] SHU Q L, WU C S, ZHONG Q X, et al. Total generalized variation-regularized variational model for single image dehazing [C]//Ninth International Conference on Graphic and Image Processing. Qingdao, China:SPIE, 2017: 106152M.
[10] KRISHNAN D, FERGUS R. Fast image deconvolution using hyper-Laplacian priors [C]//23rd Annual Conference on Neural Information Processing Systems.Vancouver, Canada: DBLP, 2009: 1033-1041.
[11] ZUO W M, MENG D Y, ZHANG L, et al. A generalized iterated shrinkage algorithm for non-convex sparse coding [C]//IEEE International Conference on Computer Vision. Sydney, Australia: IEEE, 2013: 217-224.
[12] ROERDINK J B T M. FFT-based methods for nonlinear image restoration in confocal microscopy [J]. Journal of Mathematical Imaging and Vision, 1994, 4(2):199-207.
[13] BERTERO M, BOCCACCI P. Introduction to inverse problems in imaging [M]. London, UK: IOP Publishing Ltd, 1998.
[14] BECK A, TEBOULLE M. A fast iterative shrinkagethresholding algorithm for linear inverse problems [J].SIAM Journal on Imaging Sciences, 2009, 2(1): 183-202.
[15] ZUO W M, LIN Z C. A generalized accelerated proximal gradient approach for total-variation-based image restoration [J]. IEEE Transactions on Image Processing,2011, 20(10): 2748-2759.
[16] WRIGHT S J, NOWAK R D, FIGUEIREDO M A T.Sparse reconstruction by separable approximation [J].IEEE Transactions on Signal Processing, 2009, 57(7):2479-2493.
[17] TIERNEY S, GUO Y, GAO J B. Selective multi-source total variation image restoration [C]//International Conference on Digital Image Computing: Techniques & Applications. Adelaide, Australia: IEEE, 2015: 677-684.
[18] SETZER S, STEIDL G, TEUBER T. Infimal convolution regularizations with discrete l1-type functionals[J]. Communications in Mathematical Sciences, 2011,9(3): 797-827.
[19] ONO S, YAMADA I. Optimized JPEG image decompression with super-resolution interpolation using multi-order total variation [C]//IEEE International Conference on Image Processing. Melbourne, Australia:IEEE, 2013: 474-478.
[20] SHIRAI K, OKUDA M. FFT based solution for multivariable L2 equations using KKT system via FFT and efficient pixel-wise inverse calculation [C]//IEEE International Conference on Acoustics, Speech and Signal Processing. Florence, Italy: IEEE, 2014: 2629-2633.
[21] BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers [J]. Foundations and Trends in Machine Learning, 2010, 3(1): 1-122.
[22] SIM?OES M, BIOUCAS-DIAS J, ALMEIDA L B, et al. A convex formulation for hyperspectral image superresolution via subspace-based regularization [J].IEEE Transactions on Geoscience and Remote Sensing,2015, 53(6): 3373-3388.
[23] LIU H Y, ZHANG Z R, XIAO L, et al. Poisson noise removal based on nonlocal total variation with Euler's elastica pre-processing [J]. Journal of Shanghai Jiao Tong University (Science), 2017, 22(5): 609-614.
[24] LIN T Y, MA S Q, ZHANG S Z. Iteration complexity analysis of multi-block ADMM for a family of convex minimization without strong convexity [J]. Journal of Scientific Computing, 2016, 69(1): 52-81.
[25] HONG M Y, LUO Z Q, RAZAVIYAYN M. Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems [C]//IEEE International Conference on Acoustics, Speech and Signal Processing. Brisbane, Australia: IEEE, 2015: 3836-3840.
