Total variation regularization for 3D reconstruction in fluorescence tomography: experimental phantom studies

Abstract

Fluorescence tomography (FT) is depth-resolved three-dimensional (3D) localization and quantification of fluorescence distribution in biological tissue and entails a highly ill-conditioned problem as depth information must be extracted from boundary measurements. Conventionally, L2 regularization schemes that penalize the euclidean norm of the solution and possess smoothing effects are used for FT reconstruction. Oversmooth, continuous reconstructions lack high-frequency edge-type features of the original distribution and yield poor resolution. We propose an alternative regularization method for FT that penalizes the total variation (TV) norm of the solution to preserve sharp transitions in the reconstructed fluorescence map while overcoming ill-posedness. We have developed two iterative methods for fast 3D reconstruction in FT based on TV regularization inspired by Rudin-Osher-Fatemi and split Bregman algorithms. The performance of the proposed method is studied in a phantom-based experiment using a noncontact constant-wave trans-illumination FT system. It is observed that the proposed method performs better in resolving fluorescence inclusions at different depths.

Hadamard multiplexed fluorescence tomography

“…The reconstructions are performed by multi-level scheme algebraic reconstruction technique (MLS-ART) which is a fast commonly used inverse solver that does not require optimal parameter selection [20,21] unlike regularized least-squares techniques [5,6,9]. Hence, the reconstruction algorithm (including its parameters) is the same for all data SNRs and source configurations (the relaxation parameter of MLS-ART is set to 1 in all cases).…”

“…Consequently, noise and errors in the FT data and modeling can produce significant artifacts in the 3D reconstructions. FT inverse solvers utilize regularization techniques to provide robustness and stability against noise and errors [5][6][7][8][9]. However, as the level of noise and error contamination rises, the quality of regularized reconstructions deteriorates.…”

“…However, as the level of noise and error contamination rises, the quality of regularized reconstructions deteriorates. Depending on the dynamics and nature of the inversion algorithms, different types of artifacts and errors arise in the 3D reconstructions when FT data are considerably noisy [9].…”

Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods

“…However, they led to the processing of large amounts of 3D data, which requires tremendous computational time. From the theoretical aspect, a plethora of nonlinear regularization methods have also been applied, [9][10][11][12][13][14][15][16][17] which again have caused additional complexity in computations. The non-negativity constraint in FMT reconstruction is another challenge.…”

Improved sparse reconstruction for fluorescence molecular tomography with L_1/2 regularization

“…Although these methods can deal with the ill-posedness of FMT inverse problem, the over-smoothness of L 2 -norm results in blurred or spread targets with the loss of high-frequency feature in the reconstructed images [14]. Owing to the edge-preserving properties of total variation (TV) norm, TV regularization based reconstruction methods are presented for linear and nonlinear FMT, and the numerical and experimental results therein demonstrate potential of offering higher resolution and robustness compared to conventional L 2 regularization [15][16][17].…”