High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing

Abstract

Mesoscopic fluorescence molecular tomography (MFMT) is new imaging modality aiming at 3-D imaging of molecular probes in a few millimeter thick biological samples with high-spatial resolution. In this paper, we develop a compressive sensing-based reconstruction method with l1-norm regularization for MFMT with the goal of improving spatial resolution and stability of the optical inverse problem. Three-dimensional numerical simulations of anatomically accurate microvasculature and real data obtained from phantom experiments are employed to evaluate the merits of the proposed method. Experimental results show that the proposed method can achieve 80 μm spatial resolution for a biological sample of 3 mm thickness and more accurate quantifications of concentrations and locations for the fluorophore distribution than those of the conventional methods.

Fig. 1

CCF between Jacobian (A) and the discrete Fourier transform (T) for several orders (m = 1 – 16).

Fig. 2

Vascular tree model. (a) Three-dimensional visualization with maximum projection on the bounding planes. (b) XY view. The dimensions of three components of the vascular tree are 0.4 mm × 2.8 mm × 0.4 mm, 0.7 mm × 0.3 mm × 0.3 mm, and 0.5 mm × 0.2 mm × 0.2 mm, respectively, for the main tree, bigger off shoot, and smaller off shoot. (c) yz-slices of the sensitivity matrix; seven detectors are placed along y-axis on the volume surface.

Fig. 3

Synthetic measurements for the vascular model of Fig. 2. Each pixel corresponds to a source position for a specific detector offset with the vascular model embedded at depth of (a) 0.5 mm and of (b) 3 mm (SNR of 60). The colorbar represents the spatial contrast distribution acquired by each individual detector (ΔR) normalized to the overall dynamical range of measurements (R).

Fig. 4

Reconstruction results at different depths. (a)–(c) Reconstruction results were presented for CG, LSQR, and CS at depth of 2 mm. (d)–(f) Cross section of (a)–(c); colorbars represent the quantum efficiency (η(r)). (g) Reconstruction results of three methods at six different depths. (h) Reconstruction results of CS at six different depths. (i) and (j) Three-dimensional rendering of the reconstructions for CS at 0.5 and 2.8 mm, respectively (voxel size of 100 μm and no noise added in the measurements).

Fig. 5

Reconstruction performance for 3 voxel sizes at three different depths: (a)–(c) CS reconstruction results at depth of 2 mm with voxel sizes of 200, 100, and 80 μm, respectively. (d)–(f) Cross section of (a)–(c). Colorbars represent the quantum efficiency (η(r)). (g)–(i) CG, LSQR, and CS reconstruction results of three different resolutions at depth of 1, 2, and 3 mm with different discretization levels. (j) Reconstruction result of CS with 3 voxel sizes.

Fig. 6

Reconstruction performance for ten levels of additional noise at three different depths. (a)–(c) Reconstruction results of three methods at depth of 1 mm with SNR of 40. (d)–(f) S_MSE of the three methods reconstruction results at depth of 1, 2, and 3 mm with ten levels of noise. (g) S_MSE of CS reconstruction results at depth of 1, 2, and 3 mm with ten levels of noise.

Fig. 7

Reconstruction results for complex vasculature by three regularization methods. (a) Raw data were represented in 3-D. (b) and (c) Raw data were segmented for two different sets of vascular channels, T1 and T2. (d)–(f) Segmented vessel, T1, was reconstructed by CG, LSQR, and CS, respectively. (g)–(i) Segmented vessel, T2, reconstructed by CG, LSQR, and CS, respectively (no noise added in the vascular network model).

Fig. 8

Experimental validation of CS reconstruction results in a collagen scaffold compared with microCT and CG methods. (a) Ground truth for localizations of glass wall of two capillaries in the collagen scaffold obtained from a microCT scanner. (b) and (c) Reconstruction results of CS and CG, respectively. (d) and (e) Merged 3-D images of (b) and (c) with (a). (f) Raw data and line profile for fluorescence (blue), background (green), and subtracted (red) data, respectively. (g) Line profiles from two sets of data: left and right profiles. Upper figure shows the left profile for fluorescence (blue square), background (solid green), and subtraction (red circle). Lower figure follows the same convention for right region. (h) and (i) Overlaid reconstruction of CS and CG merged with microCT, respectively, at three different slices along y-axis.