An iterative algebraic reconstruction algorithm for emission computed tomography is presented. This algorithm, called iterative filtered backprojection (IFBP), is related to the filtered backprojection (FBP) method and considers images obtained from FBP to be degraded images. Its aim is to reduce the bias and variance of FBP images without a large increase in computation. Simulations indicate that this method possesses advantages over FBP in terms of both image bias and variance. It also has advantages over the expectation maximization algorithm in terms of both computation and image bias.<<ETX>>