Sparse Regularization-Based Reconstruction for Bioluminescence Tomography Using a Multilevel Adaptive Finite Element Method

Abstract

Bioluminescence tomography (BLT) is a promising tool for studying physiological and pathological processes at cellular and molecular levels. In most clinical or preclinical practices, fine discretization is needed for recovering sources with acceptable resolution when solving BLT with finite element method (FEM). Nevertheless, uniformly fine meshes would cause large dataset and overfine meshes might aggravate the ill-posedness of BLT. Additionally, accurately quantitative information of density and power has not been simultaneously obtained so far. In this paper, we present a novel multilevel sparse reconstruction method based on adaptive FEM framework. In this method, permissible source region gradually reduces with adaptive local mesh refinement. By using sparse reconstruction with l 1 regularization on multilevel adaptive meshes, simultaneous recovery of density and power as well as accurate source location can be achieved. Experimental results for heterogeneous phantom and mouse atlas model demonstrate its effectiveness and potentiality in the application of quantitative BLT.

Hybrid Multilevel Sparse Reconstruction for a Whole Domain Bioluminescence Tomography Using Adaptive Finite Element

“…On the other hand, l 1 -norm based sparse regularization methods have attracted considerable amount of attention in BLT [10, 20–25], and the reconstructions' results therein demonstrate that l 1 -norm solution fits the sparsity nature of bioluminescent source distribution in BLT practice. Using l 1 regularization, we formulate the BLT inverse problem to the following optimization problem: $\begin{array}{c}\underset{\mathbf{S}}{\min }\frac{\mathrm{1}}{\mathrm{2}}{||AS-{\mathrm{\Phi }}^m||}_2^2+\tau {||S||}_{\mathrm{1}},\end{array}$ where ||·|| 2 denotes the Euclidean norm, ||·|| 1 is the l 1 norm, and τ > 0 is a regularization parameter.…”

Multi-modality molecular imaging for gastric cancer research

“…In our previous studies, two kinds of regularization methods were utilized as the penalty function, including the Tikhonov regularization method and the spares regularization method [9][10][11][12][13][14][15][16][17][18][19][20] . For the Tikhonov regularization, the penalty function was defined as an l 2 norm of k S ; and for the sparse regularization, the penalty function was defined as an l 1 norm.…”

“…To evaluate the performance of our home-developed tri-modality BLT/FMT/micro-CT system, we have developed some reconstruction algorithms for 3D optical imaging based on the diffusion equation (DE) and the finite element method (FEM), including the adaptive hp FEM (hp-FEM) 13 , Tikhonov regularization based truncated total least squares and multi-phase level set algorithm [14][15][16] , sparse regularization based truncated Newton interior-point method and incomplete variables truncated conjugate gradient method [17][18][19] . Furthermore, in order to deal with the problem of early gastric cancer detection, we proposed a hybrid diffusion-radiosity theory (HDRT) model based reconstruction algorithm 24 and an endoscopic algorithm 25 .…”

“…CLT is an emerging molecular imaging technology based on the well-known phenomenon of Cerenkov radiation 8 . Secondly, based on the home-developed tri-modality BLT/FMT/micro-CT system and the requirements of biomedical applications, we proposed several reconstruction algorithms for 3D optical imaging which have been well validated using the numerical simulations and small animal experiments [9][10][11][12][13][14][15][16][17][18][19][20] . In addition, based on the Monte Carlo method and free space light transport theory, we developed a simulation platform for optical imaging named molecular optical simulation environment (MOSE), which provides an accurate solution to light transport both in biological tissues and in free space 21,22 .…”

Adaptive parameter selection for Tikhonov regularization in Bioluminescence tomography

“…Hence, it is necessary to incorporate further information about the desired solution to stabilize the problem and to single out a meaningful and stable solution, which is the purpose of regularization [4][5][6][7][8][9]. Through the most well-known Tikhonov regularization method [6], a well-posed optimization problem to approximate the original BLT problem is obtained.…”