Fast image reconstruction for optical absorption tomography in media with radially symmetric boundaries

In this paper we present a reconstruction algorithm to invert the linearized problem in optical absorption tomography for objects with radially symmetric boundaries. This is a relevant geometry for functional volume imaging of body regions that are sensitive to ionizing radiation, e.g., breast and testis. From the principles of diffuse light propagation in scattering media we derive the governing integral equations describing the effects of absorption variations on changes in the measurement data. Expansion of these equations into a Neumann series and truncation of higher-order terms yields the linearized forward imaging operator. For the proposed geometry we utilize an invariance property of this operator, which greatly reduces the problem dimensionality. This allows us to compute the inverse by singular value decomposition and consequently to apply regularization techniques based on the knowledge of the singular value spectrum. The inversion algorithm is highly efficient computing slice images as fast as convolution-backprojection algorithms in computed tomography (CT). To demonstrate the capacity of the inversion scheme we present reconstruction results for synthetic and phantom measurement data.