Analysis of the Use of Unmatched Backward Operators in Iterative Image Reconstruction With Application to Three-Dimensional Optoacoustic Tomography

Due to their ability to model complicated imaging physics, to compensate for imperfect data acquisition systems, and to exploit prior information regarding the to-be-imaged object, iterative image reconstruction algorithms can often produce higher quality images than analytical reconstruction methods. However, for three-dimensional (3-D) imaging tasks with large fields of view, iterative reconstruction methods can be computationally burdensome. A common cause for this is the need to repeatedly evaluate the forward operator and its adjoint. From the algorithmic perspective, one way to accelerate iterative algorithms is to substitute the adjoint operator with an unmatched approximation of it, which can be computed more efficiently. Previous works have investigated some of the impacts of employing unmatched backward operators in iterative algorithms. This paper extends the theoretical analysis of unmatched backward operators to a more general penalized least-squares framework that allows for complex eigenvalues and regularization. Additionally, a convergence condition for a Landweber-type algorithm employing an unmatched backward operator is presented and numerically corroborated. An unmatched backward operator is introduced to accelerate iterative image reconstruction in 3-D optoacoustic tomography, and it is investigated by use of experimental data.