Image reconstruction of the absorption coefficients with l 1-norm minimization from photoacoustic measurements

Abstract

Background: The photoacoustic (PA) imaging by considering light propagation into image reconstruction process can provide quantitative information of photon absorbers, such as hemoglobin and exogenous dyes, and to improve their imaging contrasts.

Methods: A 2D image reconstruction of the distribution of the light absorption coefficient from the PA measurements with light source and ultrasound transducer placed at the identical position was tested. The PA pressures were formulated with the PA wave equation and the photon diffusion equation. The relation between the PA pressure and the absorption coefficient was linearized. The image reconstruction was carried out by minimizing the squared error between the measured and calculated PA signals. The l 1-norm of the reconstructed image was simultaneously minimized to improve the localization of the reconstructed target in the image. The image reconstruction with the l 1-norm minimization was compared to that with the Tikhonov regularization by numerical simulation and phantom experiment. In phantom experiment, an aqueous solution of the intralipid and the indocyanine green was used as the measured object. The PA probe had optical fiber for illumination and piezoelectric film for detection placed at the identical position.

Results: The l 1-norm minimization reconstructed more localized target than the Tikhonov regularization.

Conclusions: The l 1-norm minimization is useful for the sparse PA image reconstruction.

Keywords: Absorption coefficient; image reconstruction; inverse problem; photoacoustic (PA) imaging.

Figure 1

Geometrical conditions of (A) the numerical simulation and (B) the phantom experiment. PA, photoacoustic; ICG, indocyanine green.

Figure 2

The edge of the PA probe used in the phatom experiment. PA, photoacoustic.

Figure 3

Reconstructed images of μ_a (mm^–1) with (A) Reg.1 (B) Reg.2 and (C) Reg.3 in the numerical simulation.

Figure 4

Averages of SNR₁ of the reconstructed images for (A) the cases with μ_a =0.6 mm^–1 (red), 1.1 mm^–1 (green) and 1.7 mm^–1 (blue), and (B) the cases with the depths of 5 mm (red), 7 mm (green) and 9 mm (blue).

Figure 5

Averages of SNR₂ of the reconstructed images for (A) the cases with μ_a =0.6 mm^–1 (red), 1.1 mm^–1 (green) and 1.7 mm^–1 (blue), and (B) the cases with the depths of 5 mm (red), 7 mm (green) and 9 mm (blue).

Figure 6

Reconstructed images of μ_a (mm^–1) with (A) Reg.1 (B) Reg.2 and (C) Reg.3 in the phantom experiment.

Figure 7

μ_a reconstructed with Reg.1 as a function of the true μ_a in (A) the numerical simulation and (B) the phantom experiment when the depth was 5 mm (circle symbol), 7 mm (square symbol) or 9 mm (triangle symbol).