We present an algorithm for lossy compression of hyperspectral images for imple- mentation on field programmable gate arrays (FPGA). To greatly reduce the bit rate required to code images, we use linear prediction between the bands to exploit the large amount of inter-band correlation. The prediction residual is compressed using the Set Partitioning in Hierarchical Trees algorithm. To reduce the complexity of the predictive encoder, we propose a bit plane-synchronized closed loop predictor that does not require full decompression of a previous band at the encoder. The new technique achieves almost the same compression ratio as standard closed loop predictive coding and has a simpler on-board implementation.