A radiative transfer equation-based image-reconstruction method incorporating boundary conditions for diffuse optical imaging

Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging

We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel's equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface.

A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing

Fluorescence molecular tomography (FMT) is a promising tool for real time in vivo quantification of neurotransmission (NT) as we pursue in our BRAIN initiative effort. However, the acquired image data are noisy and the reconstruction problem is ill-posed. Further, while spatial sparsity of the NT effects could be exploited, traditional compressive-sensing methods cannot be directly applied as the system matrix in FMT is highly coherent. To overcome these issues, we propose and assess a three-step reconstruction method. First, truncated singular value decomposition is applied on the data to reduce matrix coherence. The resultant image data are input to a homotopy-based reconstruction strategy that exploits sparsity via ℓ₁ regularization. The reconstructed image is then input to a maximum-likelihood expectation maximization (MLEM) algorithm that retains the sparseness of the input estimate and improves upon the quantitation by accurate Poisson noise modeling. The proposed reconstruction method was evaluated in a three-dimensional simulated setup with fluorescent sources in a cuboidal scattering medium with optical properties simulating human brain cortex (reduced scattering coefficient: 9.2 cm^-1, absorption coefficient: 0.1 cm^-1) and tomographic measurements made using pixelated detectors. In different experiments, fluorescent sources of varying size and intensity were simulated. The proposed reconstruction method provided accurate estimates of the fluorescent source intensity, with a 20% lower root mean square error on average compared to the pure-homotopy method for all considered source intensities and sizes. Further, compared with conventional ℓ₂ regularized algorithm, overall, the proposed method reconstructed substantially more accurate fluorescence distribution. The proposed method shows considerable promise and will be tested using more realistic simulations and experimental setups.