Efficient reconstruction method for L1 regularization in fluorescence molecular tomography

Abstract

Fluorescence molecular tomography (FMT) is a promising technique for in vivo small animal imaging. In this paper, the sparsity of the fluorescent sources is considered as the a priori information and is promoted by incorporating L1 regularization. Then a reconstruction algorithm based on stagewise orthogonal matching pursuit is proposed, which treats the FMT problem as the basis pursuit problem. To evaluate this method, we compare it to the iterated-shrinkage-based algorithm with L1 regularization. Numerical simulations and physical experiments show that the proposed method can obtain comparable or even slightly better results. More importantly, the proposed method was at least 2 orders of magnitude faster in these experiments, which makes it a practical reconstruction algorithm.

Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method

“…For the IS_L1 method, the regularization parameter was set to 2e −5 . For the StOMP method, the parameter α was set to 0.8 and the parameter max P was set to 100, which were the same as the values used by D. Han et al [17]. For all of the reconstruction methods, the zero vector was used as the initial value of the solution.…”

“…Hence, the problem of FMT can be regarded as a sparse reconstruction problem and the fluorescent source distribution can be recovered by using sparse-type regularization (L0-norm and L1-norm) strategies. Inspired by the ideas behind the CS theory, several algorithms incorporated with L1-norm regularization have been proposed to solve the optical tomography problems in recent years [10,[13][14][15][16][17]. To preserve the sparsity of the fluorescent sources, an iteratively reweighted scheme based approach, which was able to obtain more reasonable and satisfactory results compared with the Tikhonov method was proposed [14].…”

“…Therefore, it needs a large number of iterations to reach an acceptable solution, especially when the dimension of the FMT inverse problem is quite large. To enhance the reconstruction efficiency, the stagewise orthogonal matching pursuit (StOMP) based method was introduced to conserve computation time due to the greedy pursuit strategy [17], while it needs to estimate the sparsity factor which indicates the number of unknowns in advance. There are different sparsity factors for different FMT experiments, therefore it is not always able to achieve acceptable results for estimation of the sparsity factor empirically in this method.…”

“…In addition, our method incorporates an effective technique for re-evaluating the reliability of all candidates at each iteration of the process, which guarantees the accuracy and reliability for fluorescence reconstruction. To better evaluate the proposed method, we compared it to the IS_L1 method and the StOMP method both in numerical experiments and in vivo mouse experiments [15,17]. The proposed method is proved to be more accurate, efficient, robust, and reliable for fluorescence reconstruction compared to the contrasting methods, which demonstrates its potential for practical FMT applications.…”

Effective and robust approach for fluorescence molecular tomography based on CoSaMP and SP3 model

“…17,18 Although the CS theory demonstrates that the ' 1 approach provides exact reconstruction in the noiseless case, 19 greedy methods have more advantages in computational e±ciency, especially for large-scale applications. Consequently, several greedy reconstructions based on orthogonal matching pursuit (OMP), 20 stagewise OMP (StOMP) 21 and adaptive matching pursuit (AMP) 22 have been applied to FMT. However, these greedy algorithms do not provide global convergence guarantees.…”