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# A parallel operator splitting algorithm for solving constrained total-variation retinex

• * Corresponding author: Deren Han
• An ideal image is desirable to faithfully represent the real-world scene. However, the observed images from imaging system are typically involved in the illumination of light. As the human visual system (HVS) is capable of perceiving identical color with spatially varying illumination, retinex theory is established to probe the rationale of HVS on perceiving color. In the realm of image processing, the retinex models are devoted to diminishing illumination effects from observed images. In this paper, following the recent work by Ng and Wang (SIAM J. Imaging Sci. 4:345-356, 2011), we develop a parallel operator splitting algorithm tailored for the constrained total-variation retinex model, in which all the resulting subproblems admit closed form solutions or can be tractably solved by some subroutines without any internally nested iterations. The global convergence of the novel algorithm is analysed on the perspective of variational inequality in optimization community. Preliminary numerical simulations demonstrate the promising performance of the proposed algorithm.

Mathematics Subject Classification: 65K15, 68U10, 90C30, 90C90.

 Citation:

• Figure 1.  Cartoon images for retinex

Figure 2.  Numerical results of retinex on cartoon images

Figure 3.  Numerical results of retinex on cartoon images

Figure 4.  RGB image for retinex. (a) ideal color wheel image. (b) color wheel image with illumination

Figure 5.  Numerical results of retinex on color wheel image

Figure 6.  Test RGB images for retinex. (a) $501\times328$ "Girl" image. (b) $324\times323$ "Wall" image. (c) $400\times224$ "Book" image. (d) $281\times375$ "Room" image

Figure 7.  Numerical results on "Girl" image

Figure 8.  Numerical results on "Wall" image

Figure 9.  Numerical results on "Book" image

Figure 10.  Numerical results on "Room" image

Figure 11.  The evolutions of merits $\|u^k-\hat{u}\|_2$ and $\frac{\|u^{k+1}-\hat{u}\|_2}{\|u^k-\hat{u}\|_2}$ w.r.t. iterations

Figures(11)