Fluorescence tomography of targets in a turbid medium using non-negative matrix factorization

A near-infrared optical tomography approach for detection, three-dimensional localization, and cross-section imaging of fluorescent targets in a turbid medium is introduced. The approach uses multisource probing of targets, multidetector acquisition of diffusely transmitted fluorescence signal, and a non-negative matrix factorization based blind source separation scheme to obtain three-dimensional location of the targets. A Fourier transform back-projection algorithm provides an estimate of target cross section. The efficacy of the approach is demonstrated in an experiment involving two laterally separated small fluorescent targets embedded in a human breast tissue-simulating sample of thickness 60 times the transport mean free path. The approach could locate the targets within ∼1 mm of their known positions, and provide estimates of their cross sections. The high spatial resolution, fast reconstruction speed, noise tolerance, and ability to detect small targets are indicative of the potential of the approach for detecting and locating fluorescence contrast-enhanced breast tumors in early growth stages, when they are more amenable to treatment.

Figure 1

Multidetector acquisition of fluorescence (wavelength, ${\lambda }_m$) intensity distribution on the detector plane following multisource illumination (wavelength, ${\lambda }_x$) of the source plane of the sample.

Figure 2

(a) A schematic diagram of the experimental arrangement for imaging objects embedded in a turbid medium. Key: NB = narrow-band-pass filter centered on 830 nm, TS = translational stage, CCD = charge coupled device camera, PC = personal computer, SP = source plane, DP = detector plane. Inset (below) shows the 2D array of points on the source plane that were scanned across the incident laser beam. A typical raw image is shown in the PC monitor. (b) The absorption and fluorescence spectra of ICG in water. (c) A typical raw image (left) detected by the CCD camera is cropped (middle) and binned (right).

Figure 3

(a) and (b) NCIDs corresponding to the left target on the detector plane and on the source plane, respectively; (c) and (d) least squares fits to the spatial profiles along the white dashed lines in (a) and (b), respectively.

Figure 4

(a) Cross-section image of the left target at the $z$ = 30.5 cm plane; (b) corresponding spatial profiles in the $x$ and $y$ directions along the white lines shown in (a).

Figure 5

(a) Pseudo-color images generated using analytical forward model without noise. (b) Noisy image generated by adding 50% multiplicative Gaussian noise and 50% Poisson noise. (c) Image recovered using the NMF formalism. Similar images were obtained for other combinations of noise levels.

Figure 6

Variation of PSNR with noise obtained by keeping multiplicative Gaussian noise fixed at a certain level and varying the Poisson noise level, as noted on the curves. The lines connecting the data points represented by circles and triangles are meant for guiding the eyes only.