Joint image restoration and edge detection in cooperative game formulation

Abstract Image restoration and edge detection are two fundamental problems in image processing. Detecting edges from degraded images is quite challenging. We propose a new cooperative game framework for joint image restoration and edge detection. It consists of two objective functions, one aims to detect edges from the unknown real image, the other aims to restore the unknown real image with supervision of the detected edges. The major advantage of the proposed formulation is that, it decouples the two tasks in an elegant way so that we can solve them iteratively, and the two tasks interactively facilitate each other during iteration. The novelties are twofold. First, we modify the previous edge detection model so that it detects edges from the unknown restored image. Second, for image restoration, we define a new regularity term: the weighted sparse method-noise. The method-noise is the residual of the restored image and its smoothed version, obtained by an advanced denoising method. The weight depends on detected edges from the restored image. The advantage of the new regularity is that, it penalizes sparsity of smooth areas heavy while edges much less, thus the flat areas can be smoothed sufficiently and the edges remain sharp. With mild conditions, convergence of the presented algorithm can be guaranteed. Extensive experimental results show that the proposed method outperforms other related methods in both image restoration and edge detection.