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Title:: Research on the underdetermined problem ?in 3D fluorescence imaging based on compressive sensing

Author(s):: WANG Zhangli; CHEN Chunxiao; LU Xiong; LI Dongsheng; Department of Biomedical Engineering, Nanjing University of Aeronautics and Astronautics， Nanjing 211106，China

Keywords:: Underdetermined; Compression sensing; QR-Decomposition; L1 regularization; L1/2 regularization; Sparse reconstruction

摘要:: 压缩感知理论的提出，使得小动物三维荧光断层成像中在体肿瘤的稀疏重建成为可能。然而，小动物三维荧光逆向重建过程中系数矩阵的列向量具有高度的相干性，导致了正则化问题不能得到最稀疏的解。本研究提出了基于QR分解的系数矩阵正交变换方法，以降低系数矩阵列向量的高度相干性，并通过求解L1/2正则化问题逆向重建小动物体内光源大小和位置。数值仿真和活体小鼠实验表明，该方法能够有效的降低逆向重建过程中的欠定性，提高肿瘤源重建精度。

Abstract:: The idea of compressive sensing theory makes it possible to reconstruct the tumors of animals in 3D fluorescence molecular tomography. However, the column vectors of the coefficient matrix used for 3D FMT reconstruction are highly coherent, which means the sparsest solution of the regularization of is not available. In this paper, we proposed a method to reduce the coherence of coefficient matrix based on QR-Decomposition, and realized reverse reconstruction by solving the problem of regularization. We investigated the performance of the proposed method with both simulated data and in vivo mice experimental data. The results demonstrate that the proposed method can effectively reduce the uncertainty of the tumor reverse reconstruction and improve the reconstruction accuracy.