Gradient-Free Joint Reconstruction of Initial Pressure Distribution and Wave Speeds in Transcranial Photoacoustic Computed Tomography

Transcranial photoacoustic computed tomography (PACT) shows promise as a neuroimaging modality for humans, but image reconstruction is challenging due to skull-induced aberrations in the measurement data. Traditional model-based reconstruction methods require accurate knowledge of the skull’s acoustic and elastic parameters to mitigate these. Joint reconstruction methods have been proposed to concurrently estimate the required skull parameters and initial pressure distribution. Compared to conventional model-based methods, the additional gradient computation for the skull parameters imposes a significantly higher computational burden. This study aims to develop a joint reconstruction method that does not require the gradient computation with respect to the skull parameters, enabling efficient and effective aberration compensation in three-dimensional transcranial PACT. This method assumes that the skull geometry is known from adjunct CT data and is described as a reduced-dimensionality parameterized skull model, with the skull parameters to be optimized being the compressional and shear wave speeds for the skull plate and diploë layer. The joint objective function is represented as a bi-level optimization problem, with the outer minimization problem over wave speeds subject to the inner minimization problem over the initial pressure distribution. The outer problem is then solved using a derivative-free optimization approach. The method was systematically evaluated using realistic three-dimensional head phantoms. The results establish that the proposed method can yield significantly improved image quality compared to a model-based method when the skull’s wave speeds were not known accurately. The proposed method offers an efficient approach for reconstructing images of subjects with poorly characterized skull properties.