Characterization of Sparse-Array detection Photoacoustic Tomography using the Singular Value Decomposition

A photoacoustic tomography (PAT) method that employs a sparse two-dimentional (2D) array of detector elements has recently been employed to reconstruct images of simple objects from highly incomplete measurement data. However, there remains an important need to understand what type of object features can be reliably reconstructed from such a system. In this work, we numerically compute the singular value decomposition (SVD) of different system matrices that are relevant to implementations of sparse-array PAT. For a given number and arrangement of measurement transducers, this will reveal the type of object features that can reliably be reconstructed as well as those that are invisible to the imaging system.