Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization

Abstract

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging.

The CCube reconstruction algorithm for the SoLid experiment

“…Second, the FISTA result described above is used. It has been shown [17] that the choice of the latter significantly improves, in general, the performance of ML-EM for sparse problems, and this is also observed in this work. Equation 12 defines the master formula of the ML-EM algorithm.…”

Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern

“…These sparse regularization methods mainly employ the l 1 norm of the image vector combined with other penalty terms to formulate hybrid regularization methods, such as l 1 combined with total variation regularization and l 1 combined with l 2 regularization [13]. Aside from encoding sparsity of the image as the regularizer, other regularization techniques that form regularizers using prior information of the object are also investigated including Laplacian-type regularization that incorporates tissue structural information into reconstruction [7], patch-based anisotropic diffusion regularization that solves the issue of oversmooth and noisy reconstruction [9], and maximum-likelihood expectation maximization combined with sparse regularization method that reduces background noise and promotes sparsity at the same time [29].…”

Sensitivity uniformity ratio as a new index to optimize the scanning geometry for fluorescent molecular tomography

“…Therefore, different methods were used to compensate information loss at different steps of image acquisition,[ 1 2 3 ] forward, and inverse stages. [ 4 5 ] The optimization of the source-detector geometry is one of the most practical and effective methods that have been used in recent studies. [ 6 7 ] Various methods, such as singular-value analysis[ 8 9 ] and orthogonality of the Jacobian matrix, were used to evaluate the source-detector geometries and to optimize sampling frequency, the field of view, etc.…”