A global inverse-problem approach to quantitative photo-switching optoacoustic mesoscopy

TL;DR

The paper addresses quantitative photo-switching optoacoustic mesoscopy by formulating a global inverse problem that jointly models optical switching and acoustic propagation through a matrix-free forward operator A=W_tot S. It introduces a one-step reconstruction with hybrid $l_1$-TV regularization solved by a proximal-gradient (FISTA) method and demonstrates robustness to noise and fluence mismatches, outperforming traditional two-step or unregularized approaches. The approach is validated on numerical phantoms, showing stable performance across noise levels, laser powers, and kinetic differences, and is implemented efficiently on GPUs with significant speedups via custom Row and Image Operators. The framework is extendable to 3D imaging and adaptable to various transducer impulse responses, offering a path toward cellular-resolution imaging in photo-switching OA mesoscopy.

Abstract

In this paper, we propose a global framework that includes a detailed model of the photo-switching and acoustic processes for photo-switching optoacoustic mesoscopy, based on the underlying physics. We efficiently implement two forward models as matrix-free linear operators and join them as one forward operator. Then, we reconstruct the concentration maps directly from the temporal series of acoustic signals through the resolution of one combined inverse problem. For robustness against noise and clean unmixing results, we adopt a hybrid regularization technique composed of the $l_1$ and total-variation regularizers applied to two different spaces. We use a proximal-gradient algorithm to solve the minimization problem. Our numerical results show that our regularized one-step approach is the most robust in terms of noise and experimental setup. It consistently achieves higher-quality images, as compared to two-step or unregularized methods.

Figures (9)

• Figure 1: (Left) Experimental setup. The sample being imaged is represented by the gray object. The orange and green discs represent two species of photo-switching reporters. The pink area represents the diffuse illumination from the laser. The sensitivity field of two arbitrary transducers in the array of detectors is depicted by the blue areas. (Right) Principle of photo-switching. The OFF and ON switching cycles (also wavelengths used in the cycle) are indicated by color red and magenta, respectively. On top, the numbers on the lasers represent the pulse number within a cycle. On the bottom, $t_1, t_2, \ldots, t_N$ represent the discrete time points during a switching cycle. Dashed curves with the same color-code as the reporters during the OFF cycle illustrate the evolution of the amplitude of the OA signal. The dashed gray horizontal line indicates the evolution of a point in the background.
• Figure 2: Forward pipeline and inversion approaches.
• Figure 3: (a) Spatial response of the transducer. The blue area represents the sensitivity field of the transducer. The dots represent the center of the transducer (T), the focal spot (F) and a point OA source (M). (b)-(f) Generation of the acoustic signals. SPR: spatial response of the transducer. EIR: electrical impulse response of the transducer. (b) and (b'): Sample. The background is in gray, the green and orange discs represent two photo-switching reporters. The dashed horizontal red line represents the location of the focal plane. The dashed gray lines in (b) and (b') indicate the horizontal line of pixels of interest, one above (b) and one below (b') the focal plane. (c) and (c'): Masked SPR (map of the weighted curves that corresponds to the depth of interest in (b) and (b'), respectively). (d) and (d'): Correlation between the sample and the masked SPR (c) and (c'). The focal plane (red dashed line) indicates where to extract the line of pixels. (e) Spatial integration step by stacking the extracted lines at the corresponding locations indicated in (b) and (b'). The narrow vertical box indicates a line of pixels on which we convolve with the EIR of the transducer (f).
• Figure 4: (a)-(c) Ground-truth concentration maps of the two photo-switching species of reporters and the non-switching background. The unit is $\mu$M (micromolar). The insets of two of the reporters are shown in (a) and (b) for better visualization. The horizontal dotted line in (c) indicates the position of the focal plane of the transducer. (d) Computed fluence map (arbitrary unit) used for reconstruction. (e) True fluence map (arbitrary unit) used to synthesize measurements. (f) Difference map between (d) and (e) in percentage. (g) Synthesized OA signals (first frame) during an OFF-switching cycle. Each reporter is circled out for better identification. (h) Temporal series of the OA signals (intensity averaged over the area of each reporter). The color coding is the same as in (g), similar for (j) and (l). (i) and (k): Subsequent acoustic signals (first frame) with 1% (i) and 10% (k) noise. (j) and (l): Temporal series of the acoustic signals (intensity averaged over the area of each reporter) that correspond to (i) and (k).
• Figure 5: Reconstructed concentration maps using the regularized two-step ((a)-(c)) and one-step ((d)-(f))approaches under 1% noise level. (g)-(i) Ground truth. The rectangular region between the two horizontal dashed lines in (g) indicates the area on which we calculate the SSIM.