Abstract
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.
Highlights
As an important optical molecular imaging modality, fluorescence molecular tomography (FMT) is a non-invasive molecular imaging technology that can observe imaging targets quantitatively at the molecular level [1]
To quantitatively evaluate the accuracy of the proposed reconstruction method for both source location and shape recovery, several indices including location error (LE), contrast-to-noise ratio (CNR), normalized mean square error (NMSE), reconstructed fluorescent yield (RFY), Dice index and Time were calculated in this study
The in vivo experiment further demonstrated that the correntropy-induced metric with a Laplacian kernel (CIML) method considerably improves the performance of FMT reconstruction, which means that the CIML method has excellent potential for biological applications
Summary
As an important optical molecular imaging modality, fluorescence molecular tomography (FMT) is a non-invasive molecular imaging technology that can observe imaging targets quantitatively at the molecular level [1]. FMT allows visualization of the 3D distribution of fluorescent probes in the tissue by solving the linear system of equations between a system matrix and the measured values of surface photons. Due to the strong scattering property of biological tissues and the limited boundary measurements with noise, the reconstruction problem in FMT is severely ill-posed. The error term measures empirical loss, and the regularization term encourages sparsity of the signal. Based on finite element analysis, the measurements that cannot be observed are removed and a linear relationship between the unknown fluorescent source within the tissue and the surface photon density is established. Given the noise in the FMI measurement and the ill-posed problem in the weight matrix A, it is impractical to solve x directly. The traditional sparse reconstruction model with l0 regularization is as follow: arg min x
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