Depth-resolved localization and quantification of fluorescence distribution in tissue, called Fluorescence Molecular
Tomography (FMT), is highly ill-conditioned as depth information should be extracted from limited number of
surface measurements. Inverse solvers resort to regularization algorithms that penalize Euclidean norm of the
solution to overcome ill-posedness. While these regularization algorithms offer good accuracy, their smoothing
effects result in continuous distributions which lack high-frequency edge-type features of the actual fluorescence
distribution and hence limit the resolution offered by FMT. We propose an algorithm that penalizes the total
variation (TV) norm of the solution to preserve sharp transitions and high-frequency components in the
reconstructed fluorescence map while overcoming ill-posedness. The hybrid algorithm is composed of two levels: 1)
An Algebraic Reconstruction Technique (ART), performed on FMT data for fast recovery of a smooth solution that
serves as an initial guess for the iterative TV regularization, 2) A time marching TV regularization algorithm,
inspired by the Rudin-Osher-Fatemi TV image restoration, performed on the initial guess to further enhance the
resolution and accuracy of the reconstruction. The performance of the proposed method in resolving fluorescent
tubes inserted in a liquid tissue phantom imaged by a non-contact CW trans-illumination FMT system is studied and
compared to conventional regularization schemes. It is observed that the proposed method performs better in
resolving fluorescence inclusions at higher depths.
We present an efficient model for the simulation of spatially incoherent sources based on Wiener chaos expansion (WCE) method with two orders of magnitude shorter simulation time over the brute-force model. In this model the stochastic wave propagation equation is reduced to a set of deterministic partial differential equations (PDEs) for the expansion coefficients. We further numerically solve these deterministic PDEs by finite difference time domain (FDTD) technique. While the WCE method is general, we apply it to the analysis of photonic crystal spectrometers for diffuse source spectroscopy.
In , we have proposed two total variation (TV) minimization wavelet models for the problem of filling in missing or damaged wavelet coefficients due to lossy image transmission or communication. The proposed models can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies. In this paper, we investigate a modification of the model for noisy images to further improve the recovery properties by using multi-level parameters in the fitting term. Some new numerical examples are also shown to illustrate the effectiveness of the recovery.