Results in non-iterative MAP reconstruction for optical tomography

Abstract

Maximum a posteriori (MAP) estimation has been shown to be an effective method for reconstructing images from optical diffusion tomography data. However, one disadvantage of MAP reconstruction is that it typically requires the use of iterative methods which are computationally intensive. However, the direct reconstruction of MAP images is possible when the forward model is linear (or linearized) and the noise and image prior are assumed Gaussian. These non-iterative MAP reconstruction techniques only require the multiplication of an inverse matrix by a data vector to compute the reconstruction, but they depend on a combination of lossy source coding techniques and sparse matrix transforms to make the required matrix-vector product computation both computationally and memory efficient. In this paper, we show examples of how non-iterative MAP reconstruction methods can be used to dramatically reduce computation and storage for MAP reconstruction. Simulations of fluorescence optical diffusion tomography (FODT) measurements and corresponding reconstructions are used to demonstrate the potential value of these techniques. Numerical examples show the non-iterative MAP reconstruction can substantially reduce both storage and computation, as compared to traditional iterative reconstruction methods.