Correntropy-induced metric with Laplacian kernel for robust fluorescence molecular tomography

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 l ₂-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 l ₀-norm and l ₁-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.