论文标题
剩余求解器及其展开的神经网络，用于总变异正规化模型
A Residual Solver and Its Unfolding Neural Network for Total Variation Regularized Models
论文作者
论文摘要
本文建议通过找到输入和未知最佳解决方案之间的残差来解决总变异正规模型。在分析了先前的方法之后，我们开发了一种新的迭代算法，称为残留求解器，该算法在梯度域中隐式求解该模型。从理论上讲，我们在算法中证明了梯度领域的独特性。我们进一步确认，残差求解器可以在500个自然图像上达到与经典方法相同的全局最佳解。此外，我们将迭代算法展开到卷积神经网络（称为残留求解器网络）中。该网络是无监督的，可以被视为我们迭代算法的“增强版本”。最后，所提出的算法和神经网络均成功应用于几个问题，以证明它们的有效性和效率，包括图像平滑，denoing和生物医学图像重建。提出的网络是一般的，可以应用于解决其他总变异正规化模型。
This paper proposes to solve the Total Variation regularized models by finding the residual between the input and the unknown optimal solution. After analyzing a previous method, we developed a new iterative algorithm, named as Residual Solver, which implicitly solves the model in gradient domain. We theoretically prove the uniqueness of the gradient field in our algorithm. We further numerically confirm that the residual solver can reach the same global optimal solutions as the classical method on 500 natural images. Moreover, we unfold our iterative algorithm into a convolution neural network (named as Residual Solver Network). This network is unsupervised and can be considered as an "enhanced version" of our iterative algorithm. Finally, both the proposed algorithm and neural network are successfully applied on several problems to demonstrate their effectiveness and efficiency, including image smoothing, denoising, and biomedical image reconstruction. The proposed network is general and can be applied to solve other total variation regularized models.
