On 퓁1 Data Fitting and Concave Regularization for Image Recovery
On 퓁1 Data Fitting and Concave Regularization for Image Recovery
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DOI：
10.1137/10080172x
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
M. Nikolova;M. Ng;Chi-Pan Tam
中科院分区：
文献类型：
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作者：
M. Nikolova;M. Ng;Chi-Pan Tam
我们提出了一系列用于信号和图像恢复的新成本函数：它们由 $\ell_1$ 数据拟合项与凹正则化相结合组成。我们展示何时以及如何使用此类成本函数。我们的理论结果表明，这些成本函数的最小值使得它们的每个条目要么参与精确数据拟合组件，要么参与正则化部分的空组件。这是一个强大且特殊的属性，可用于解决各种图像恢复问题。这种成本函数的最小化提出了计算挑战。我们提出了一种快速最小化算法来解决这个数值问题。实验结果表明了该算法的有效性。所有的插图和数值实验都展示了这个新的成本函数系列的最小化器在解决专门的图像处理任务时所提供的可能性。
We propose a new family of cost functions for signal and image recovery: they are composed of $\ell_1$ data fitting terms combined with concave regularization. We exhibit when and how to employ such cost functions. Our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. This is a strong and particular property that can be useful for various image recovery problems. The minimization of such cost functions presents a computational challenge. We propose a fast minimization algorithm to solve this numerical problem. The experimental results show the effectiveness of the proposed algorithm. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks.