A Linear State Space Model for Photoacoustic Imaging in an Acoustic Attenuating Media

TL;DR

This paper introduces a linear state space model for photoacoustic imaging that accounts for acoustic attenuation and laser modulation, improving the accuracy of internal absorption reconstruction in complex media.

Contribution

It presents a novel state space reformulation of wave propagation equations incorporating frequency-dependent attenuation and laser modulation optimization.

Findings

Model accounts for acoustic attenuation and inhomogeneous absorption.

Optimized laser modulation enhances reconstruction accuracy.

Method outperforms traditional short pulse and chirp modulation approaches.

Abstract

In photoacoustic imaging, ultrasound waves generated by a temperature rise after illumination of light absorbing structures are measured on the sample surface. These measurements are then used to reconstruct the optical absorption. We develop a method for reconstructing the absorption inside the sample based on a discrete linear state space reformulation of a partial differential equation that describes the propagation of the ultrasound waves. Fundamental properties of the corresponding state space model such as stability, observability and controllability are also analyzed. By using Stokes' equation, the frequency dependent attenuation of the ultrasound waves is incorporated into our model, therefore the proposed method is of general nature. As a consequence, this approach allows for inhomogeneous probes with arbitrary absorption profiles and it accounts for the decrease in laser intensity due to absorption. Furthermore, it provides a method for optimizing the laser modulation signal such that the accuracy of the estimated absorption profile is maximized. Utilizing the optimized laser modulation signal yields an increase in reconstruction accuracy compared to short laser pulses as well as chirp modulation in many scenarios.