A fast and effective reconstruction method for fluorescence molecular tomography based on sparsity adaptive subspace pursuit

Fluorescence molecular tomography (FMT), which is a promising tomographic method for in vivo small animal imaging, has many successful applications. However, FMT reconstruction is usually an ill-posed problem because only the photon distribution over the body surface is measurable. The Lp-norm regularization is generally adopted to stabilize the solution, which can be regarded as a type of a priori information of the fluorescent probe bio-distribution. When FMT is used for the early detection of tumors, an important feature is the sparsity of the fluorescent sources because tumors are usually very small and sparse at early stage. Considering this, we propose a fast and effective method with L1-norm based on sparsity adaptive subspace pursuit to solve the FMT problem in this paper. Our proposed method treats FMT problem with sparsity-promoting L1-norm as the basis pursuit problem. At each iteration, a sparsity factor that indicates the number of unknowns is estimated and updated adaptively. Then our method seeks a small index set which indicates atoms exhibiting highest correlation with the current residual, and updates the current supporting set by merging the newly selected index set. It can be regarded as a kind of sparse approximation reconstruction strategy. To evaluate our proposed method, we compare it to the iterated-shrinkage-based method with L1-norm regularization in numerical experiments. The results demonstrate that the proposed algorithm is able to obtain satisfactory reconstruction results. In addition, the proposed method is about two orders of magnitude faster compared to the iterated-shrinkage-based method. Our method is a practical and effective FMT reconstruction method.