Spatially variant regularization based on model resolution and fidelity embedding characteristics improves photoacoustic tomography

Photoacoustic tomography tends to be an ill-conditioned problem with noisy limited data requiring imposition of regularization constraints, such as standard Tikhonov (ST) or total variation (TV), to reconstruct meaningful initial pressure rise distribution from the tomographic acoustic measurements acquired at the boundary of the tissue. However, these regularization schemes do not account for nonuniform sensitivity arising due to limited detector placement at the boundary of tissue as well as other system parameters. For the first time, two regularization schemes were developed within the Tikhonov framework to address these issues in photoacoustic imaging. The model resolution, based on spatially varying regularization, and fidelity-embedded regularization, based on orthogonality between the columns of system matrix, were introduced. These were systematically evaluated with the help of numerical and in-vivo mice data. It was shown that the performance of the proposed spatially varying regularization schemes were superior (with at least 2 dB or 1.58 times improvement in the signal-to-noise ratio) compared to ST-/TV-based regularization schemes.