Fluorescence molecular tomography (FMT), which is used to visualize the three-dimensional distribution of fluorescence probe in small animals via the reconstruction method, has become a promising imaging technique in preclinical research. However, the classical reconstruction criterion is formulated based on the squared l₂-norm distance metric, leaving it prone to being influenced by the presence of outliers. In this study, we propose a robust distance based on the correntropy-induced metric with a Laplacian kernel (CIML). The proposed metric satisfies the conditions of distance metric function and contains first and higher order moments of samples. Moreover, we demonstrate important properties of the proposed metric such as nonnegativity, nonconvexity, and boundedness, and analyze its robustness from the perspective of M-estimation. The proposed metric includes and extends the traditional metrics such as l₀-norm and l₁-norm metrics by setting an appropriate parameter. We show that, in reconstruction, the metric is a sparsity-promoting penalty. To reduce the negative effects of noise and outliers, a novel robust reconstruction framework is presented with the proposed correntropy-based metric. The proposed CIML model retains the advantages of the traditional model and promotes robustness. However, the nonconvexity of the proposed metric renders the CIML model difficult to optimize. Furthermore, an effective iterative algorithm for the CIML model is designed, and we present a theoretical analysis of its ability to converge. Numerical simulation and in vivo mouse experiments were conducted to evaluate the CIML method’s performance. The experimental results show that the proposed method achieved more accurate fluorescent target reconstruction than the state-of-the-art methods in most cases, which illustrates the feasibility and robustness of the CIML method.

中文翻译：

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具有拉普拉斯核的相关熵诱导度量用于稳健的荧光分子断层扫描

荧光分子断层扫描（FMT）通过重建方法将荧光探针在小动物体内的三维分布可视化，已成为临床前研究中一种很有前景的成像技术。然而，经典的重建标准是基于平方l ₂制定的-范数距离度量，使其容易受到异常值存在的影响。在这项研究中，我们提出了一个基于具有拉普拉斯核（CIML）的相关熵诱导度量的鲁棒距离。所提出的度量满足距离度量函数的条件并且包含样本的一阶和高阶矩。此外，我们展示了所提出度量的重要属性，例如非负性、非凸性和有界性，并从 M 估计的角度分析了其鲁棒性。建议的度量标准包括并扩展了传统的度量标准，例如l ₀ -norm 和l ₁-norm metrics 通过设置适当的参数。我们表明，在重建中，度量是稀疏促进惩罚。为了减少噪声和异常值的负面影响，提出了一种新颖的鲁棒重建框架，其中包含所提出的基于相关熵的度量。提出的 CIML 模型保留了传统模型的优点并提高了鲁棒性。然而，所提出的度量的非凸性使得 CIML 模型难以优化。此外，还设计了一种有效的 CIML 模型迭代算法，并对其收敛能力进行了理论分析。进行了数值模拟和体内小鼠实验以评估 CIML 方法的性能。