Abstract In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by Γ-convergence or relaxation of regularized functionals. A central tool is a capped fractional maximal function of the derivative of BV functions.

中文翻译：

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双相图像恢复

摘要在本文中，我们探讨了双相泛函在图像处理环境中的潜力。为此，我们研究了具有有界变化的函数的双相能量的最小值，并表明该能量可以通过 Γ-收敛或正则化泛函的弛豫获得。中心工具是 BV 函数导数的带上限分数极大函数。