Beck Amir, Teboulle Marc
Department of Industrial Engineering and Management, The Technion-Israel Institute of Technology, Haifa 32000, Israel.
IEEE Trans Image Process. 2009 Nov;18(11):2419-34. doi: 10.1109/TIP.2009.2028250. Epub 2009 Jul 24.
This paper studies gradient-based schemes for image denoising and deblurring problems based on the discretized total variation (TV) minimization model with constraints. We derive a fast algorithm for the constrained TV-based image deburring problem. To achieve this task, we combine an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA) we have recently introduced. The resulting gradient-based algorithm shares a remarkable simplicity together with a proven global rate of convergence which is significantly better than currently known gradient projections-based methods. Our results are applicable to both the anisotropic and isotropic discretized TV functionals. Initial numerical results demonstrate the viability and efficiency of the proposed algorithms on image deblurring problems with box constraints.
本文研究基于具有约束的离散总变分（TV）最小化模型的图像去噪和去模糊问题的梯度基格式。我们推导了一种用于基于约束TV的图像去模糊问题的快速算法。为完成此任务，我们将著名的去噪问题对偶方法的加速与我们最近引入的快速迭代收缩/阈值算法（FISTA）的一种新颖单调版本相结合。所得的基于梯度的算法兼具显著的简单性以及已证明的全局收敛速率，该收敛速率明显优于目前已知的基于梯度投影的方法。我们的结果适用于各向异性和各向同性离散TV泛函。初步数值结果证明了所提算法在具有盒约束的图像去模糊问题上的可行性和有效性。
