AUGMENTED LAGRANGIAN METHOD FOR TOTAL VARIATION RESTORATION WITH NON-QUADRATIC FIDELITY
AUGMENTED LAGRANGIAN METHOD FOR TOTAL VARIATION RESTORATION WITH NON-QUADRATIC FIDELITY
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DOI：
10.3934/ipi.2011.5.237
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发表时间：
2011-02
影响因子：
1.3
通讯作者：
Chunlin Wu;Juyong Zhang;X. Tai
中科院分区：
文献类型：
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作者：
Chunlin Wu;Juyong Zhang;X. Tai
最近增广拉格朗日方法已成功地应用于图像恢复。我们扩展的方法，全变差（TV）的恢复模型与非二次型。我们将首先介绍的方法，并提出了一个迭代算法的电视恢复具有相当一般的保真度。在每次迭代中，需要解决三个子问题，其中两个可以通过快速傅立叶变换（FFT）实现或闭合形式解决方案非常有效地解决。一般来说，第三个子问题需要迭代求解器。然后，我们将我们的方法应用到电视恢复与$L^1$和Kullback-Leibler（KL）的清晰度，两个常见的和重要的数据项去模糊图像破坏的脉冲噪声和泊松噪声，分别。对于这些典型的问题，我们证明了第三个子问题也有封闭形式的解决方案，从而可以有效地解决。此外，还给出了算法的收敛性分析.数值实验证明了该方法的有效性。
Recently augmented Lagrangian method has been successfully applied to image restoration. We extend the method to total variation (TV) restoration models with non-quadratic fidelities. We will first introduce the method and present an iterative algorithm for TV restoration with a quite general fidelity. In each iteration, three sub-problems need to be solved, two of which can be very efficiently solved via Fast Fourier Transform (FFT) implementation or closed form solution. In general the third sub-problem need iterative solvers. We then apply our method to TV restoration with $L^1$ and Kullback-Leibler (KL) fidelities, two common and important data terms for deblurring images corrupted by impulsive noise and Poisson noise, respectively. For these typical fidelities, we show that the third sub-problem also has closed form solution and thus can be efficiently solved. In addition, convergence analysis of these algorithms are given. Numerical experiments demonstrate the efficiency of our method.