Nonconvex reconstruction for low-dimensional fluorescence molecular tomographic poisson observations

As an emerging near-infrared molecular imaging modality, fluorescence molecular tomography (FMT) has great potential in resolving the molecular and cellular processes in 3D objects through the reconstruction of the injected fluorescence probe concentration. In practice, when a charge-coupled device (CCD) camera is used to obtain FMT measurements, the observations are corrupted by noise which follows a Poisson distribution. To reconstruct the original concentration, the standard least-squares function for data-fitting is not a suitable objective function to minimize since this model assumes measurement noise which follows a Gaussian distribution. Rather, in this paper, we minimize a negative log-likelihood function to more accurately model the CCD camera shot noise. Furthermore, we exploit the presence of the flourescence in only small regions of the 3D object by introducing a non-convex penalty term that promotes sparsity in the reconstruction. This paper proposes a method to solve the FMT reconstruction problem from low-dimensional and low-mean photon count measurements. Using simulated data, we validate the effectiveness of the proposed non-convex Poisson-based reconstruction method for FMT inverse problems.