Fast minimum variance estimator for limited angle CT image reconstruction

Many applications of diagnostic cross sectional imaging require that images be reconstructed from a limited number of projections (limited angle). Convolution back projection has been unsuitable in these applications. Methods for reconstruction based on stochastic estimation theory, such as the minimum variance estimator, use a discrete linear measurement model and are suitable for limited angle reconstruction. Unfortunately, the computational requirements of these methods have precluded their use. In this paper, starting from the general minimum variance estimator x = RxyRyy-1y, a computationally efficient (fast) estimator is derived for limited angle reconstruction by choosing Rxy and Ryy in the simplest way consistent with the geometric considerations of data acquisition. Minimum variance has in the past been precluded from use by the large amount of computation required to compute Ryy-1. With the fast estimator, the computation is avoided because Ryy has a particular form that allows factorization of the matrix into a product of matrices, each of which is easily inverted. A demonstration of the estimator for the reconstruction of sharp peaks is provided. Image quality is similar to that obtained with other methods.