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Retinex based on exponent-type total variation scheme

The work is supported by the 1000 Talents Program for Young Scientists of China, the Ministry of Science and Technology of China ("863" Program: 2015AA020101), and NSFC 11701418 and 11526208. Dr. Z.-F. Pang was partially supported by National Basic Research Program of China (973 Program No.2015CB856003) and NSFC (Nos.U1304610 and 11401170), and also gratefully acknowledges financial support from China Scholarship Council(CSC) as a research scholar to visit the University of Liverpool from August 2017 to August 2018.
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  • Retinex theory deals with compensation for illumination effects in images, which has a number of applications including Retinex illusion, medical image intensity inhomogeneity and color image shadow effect etc.. Such ill-posed problem has been studied by researchers for decades. However, most exiting methods paid little attention to the noises contained in the images and lost effectiveness when the noises increase. The main aim of this paper is to present a general Retinex model to effectively and robustly restore images degenerated by both illusion and noises. We propose a novel variational model by incorporating appropriate regularization technique for the reflectance component and illumination component accordingly. Although the proposed model is non-convex, we prove the existence of the minimizers theoretically. Furthermore, we design a fast and efficient alternating minimization algorithm for the proposed model, where all subproblems have the closed-form solutions. Applications of the algorithm to various gray images and color images with noises of different distributions yield promising results.

    Mathematics Subject Classification: 80M30, 80M50, 68U10.


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  • Figure 1.  Performances of four methods on $T_1$-weighted brain MR images with different levels of noises

    Figure 2.  Comparison among the four methods in terms of PSNR and MSSIM for images with different intensity inhomogeneities

    Figure 3.  Performances of four methods on $T_1$-weighted brain images with different intensity inhomogeneities

    Figure 4.  Ground truth and estimated bias field of the proposed method with examples in FIGURE 3

    Figure 5.  Comparison of the performance in terms of CV(%)

    Figure 6.  The relative errors of $r$ and $l$ and numerical energy of our model for the first image in FIGURE 3

    Figure 7.  Tests on real MR images. The parameters used in our model are $\alpha = 0.03$ and $\beta = 0.015$

    Figure 8.  Tests on color images of HoTVL1 model and our model

    Figure 9.  Decomposition of the checkboard image

    Figure 10.  Decomposition of the logvi image

    Figure 11.  Denoising and decomposition of the images containing Poisson noise

    Table 1.  PSNR and MSSIM of $T_1$-weighted brain MR images with different levels of noises

    $3\%$ $5\%$ $7\%$ $9\%$
    Test Image1 TVH1 26.8369 0.9436 25.2879 0.9174 24.4622 0.8933 23.2509 0.8629
    HoTVL1 29.7605 0.9515 27.4964 0.9342 26.6143 0.9214 25.2707 0.9063
    L0MS 29.6193 0.9198 27.4895 0.9033 26.1466 0.8915 24.3937 0.8650
    ETV 32.6749 0.9904 31.1170 0.9844 29.1291 0.9767 28.4244 0.9686
    Test Image2 TVH1 27.3897 0.9229 26.4466 0.8932 25.4457 0.8655 23.7962 0.8334
    HoTVL1 29.5698 0.9321 28.7948 0.9142 27.1248 0.8988 25.4362 0.8833
    L0MS 31.8155 0.9227 28.5140 0.8950 27.1074 0.8746 24.8900 0.8374
    ETV 33.4328 0.9911 31.4092 0.9842 29.8200 0.9764 28.6543 0.9698
     | Show Table
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