  For photoacoustic image reconstruction, certain parameters such as sensor
positions and speed of sound have a major impact in the reconstruction process
and must be carefully determined before data acquisition. Uncertainties in
these parameters can lead to errors produced by a modeling mismatch, hindering
the reconstruction process and severely affecting the resulting image quality.
Therefore, in this work we study how modeling errors arising from uncertainty
in sensor locations affect the images obtained by matrix model-based
reconstruction algorithms based on time domain and frequency domain models of
the photoacoustic problem. The effects on the reconstruction performance with
respect to the uncertainty in the knowledge of the sensors location is compared
and analyzed both in a qualitative and quantitative fashion for both time and
frequency models. Ultimately, our study shows that the frequency domain
approach is more sensitive to this kind of modeling errors. These conclusions
are supported by numerical experiments and a theoretical sensitivity analysis
of the mathematical operator for the direct problem.
