Adaptive parameter selection for Tikhonov regularization in Bioluminescence tomography

Abstract

Reconstruction of the bioluminescent source information in small animals in vivo is the inverse problem of Bioluminescence tomography (BLT), which is proved severely illposed. Regularization plays an important role in BLT, and choosing the right amount of regularization is crucial to get a meaningful result. However, automated methods to choose a regularization parameter have not been sufficiently considered to date. In this paper, we present an adaptive parameter selection method and compare it with three existing methods: L-Curve Generalized cross-validation (GCV), and Normalized Cumulative Periodogram (NCP). The proposed method was validated by numerical simulation of a heterogeneous phantom experiment. The reconstructed results suggest that the adaptive parameter choosing method perform best and combined with Tikhonov regularization it can achieve accurate localization of bioluminescent source.

A Finite Element Mesh Aggregating Approach to Multiple-Source Reconstruction in Bioluminescence Tomography

“…In this paper, the regularization parameter for Tikhonov method was determined with the adaptive method proposed in [28]. As for l 1– ls , the parameter λ was chosen as suggested in [27], that is, λ = 0.1||2 A T Φ*|| ∞ .…”

“…It is known that regularization parameter is crucial to yield a good solution for ill-posed problems, and the choice of regularization parameter is usually nontrivial. In this paper, the regularization parameter for Tikhonov method was determined with the adaptive method proposed in [ 28 ]. As for l 1– ls , the parameter λ was chosen as suggested in [ 27 ], that is, λ = 0.1||2 A T Φ*|| ∞ .…”

Research on mouse tissue classification in bioluminescence tomography forward problem

“…However, due to the complexity of solving the equation, we normally transform it into the diffusion equation [12].…”