An Efficient Numerical Method for General $L_{p}$ Regularization in Fluorescence Molecular Tomography

Reconstruction algorithms for fluorescence tomography have to address two crucial issues: 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general
Lp
regularization (
p
¿ 1). The originality of this work lies in the application of general
Lp
constraints to fluorescence tomography, combined with an efficient matrix-free strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (
L

₁
). We validate the adequacy of
L

₁
regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments.