Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography. (3rd March 2021)

• Record Type: Journal Article
• Authors: Gupta, Madhu; Kumar Mishra, Rohit; Roy, Souvik
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-03
• Subjects: inverse problems -- PDE-constrained optimization -- proximal methods -- sparsity patterns -- two-photon photoacoustic tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abdd0f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in the photoacoustic computed tomography (PACT). This framework comprises of minimizing an objective functional involving a least squares fit of the interior pressure field data corresponding to two boundary source functions, where the absorption coefficients and the photon density are related through a semi-linear elliptic partial differential equation (PDE) arising in photoacoustic tomography. Further, the objective functional consists of an L 1 regularization term that promotes sparsity patterns in absorption coefficients. The motivation for this framework primarily comes from some recent works related to solving inverse problems in acousto-electric tomography and current density impedance tomography. We provide a new proof of existence and uniqueness of a solution to the semi-linear PDE. Further, a proximal method, involving a Picard solver for the semi-linear PDE and its adjoint, is used to solve the optimization problem. Several numerical experiments are presented to demonstrate the effectiveness of the proposed framework.