For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for nonlinear, iterative decoding. Our decoder, which works with any encoder, employs self-connected memory units that make use of causal and non-causal spatial context information to progressively reduce reconstruction error over a fixed number of steps. We experiment with variants of our estimator and find that iterative refinement consistently creates lower distortion images of higher perceptual quality compared to other approaches. Specifically, on the Kodak Lossless True Color Image Suite, we observe as much as a 0.871 decibel (dB) gain over JPEG, a 1.095 dB gain over JPEG 2000, and a 0.971 dB gain over a competitive neural model.