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In photoacoustic imaging, ultrasound waves generated by a temperature riseafter illumination of light absorbing structures are measured on the samplesurface. These measurements are then used to reconstruct the opticalabsorption. We develop a method for reconstructing the absorption inside thesample based on a discrete linear state space reformulation of a partialdifferential equation that describes the propagation of the ultrasound waves.Fundamental properties of the corresponding state space model such asstability, observability and controllability are also analyzed. By usingStokes' equation, the frequency dependent attenuation of the ultrasound wavesis incorporated into our model, therefore the proposed method is of generalnature. As a consequence, this approach allows for inhomogeneous probes witharbitrary absorption profiles and it accounts for the decrease in laserintensity due to absorption. Furthermore, it provides a method for optimizingthe laser modulation signal such that the accuracy of the estimated absorptionprofile is maximized. Utilizing the optimized laser modulation signal yields anincrease in reconstruction accuracy compared to short laser pulses as well aschirp modulation in many scenarios.

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