Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing

Fluorescence diffuse optical tomography (FDOT) is an emerging molecular imaging modality that uses near infrared light to excite the fluorophore injected into tissue; and to reconstruct the fluorophore concentration from boundary measurements. The FDOT image reconstruction is a highly ill-posed inverse problem due to a large number of unknowns and limited number of measurements. However, the fluorophore distribution is often very sparse in the imaging domain since fluorophores are typically designed to accumulate in relatively small regions. In this paper, we use compressive sensing (CS) framework to design light illumination and detection patterns to improve the reconstruction of sparse fluorophore concentration. Unlike the conventional FDOT imaging where spatially distributed light sources illuminate the imaging domain one at a time and the corresponding boundary measurements are used for image reconstruction, we assume that the light sources illuminate the imaging domain simultaneously several times and the corresponding boundary measurements are linearly filtered prior to image reconstruction. We design a set of optical intensities (illumination patterns) and a linear filter (detection pattern) applied to the boundary measurements to improve the reconstruction of sparse fluorophore concentration maps. We show that the FDOT sensing matrix can be expressed as a columnwise Kronecker product of two matrices determined by the excitation and emission light fields. We derive relationships between the incoherence of the FDOT forward matrix and these two matrices, and use these results to reduce the incoherence of the FDOT forward matrix. We present extensive numerical simulation and the results of a real phantom experiment to demonstrate the improvements in image reconstruction due to the CS-based light illumination and detection patterns in conjunction with relaxation and greedy-type reconstruction algorithms.