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

Abstract

Photoacoustic tomography tends to be an ill-conditioned problem with noisy limited data, requiring imposition of regularization constraints like standard Tikhonov or total-variation to reconstruct meaningful initial pressure rise distribution from the tomographic acoustic measurements acquired at the boundary of the tissue. However, these regularization schemes does not account for non-uniform sensitivity arising due to limited detector placement at the boundary of tissue as well as other system parameters. For the first time, in this work, two regularization schemes were developed within the Tikhonov framework to address these issues in photoacoustic imaging. The model-resolution, based spatially varying regularization, and fidelity embedded regularization, based on orthogonality between the columns of system matrix were introduced in this work. 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 atleast 2 dB or 1.58 times improvement in the SNR) compared to standard Tikhonov/total-variation based regularization schemes.