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An image coding system is proposed in which hexagonally sampled images are decomposed into subbands that are selective in both frequency and orientation. Nine high frequency bands each of one octave and 60 degrees of angular orientation are built on a pyramidal structure along with one low frequency band. Bits are then allocated optimally to the subbands under a mean-squared error distortion measure. Optimal quantizers are designed for each subband for entropy coding under a Laplacian distribution assumption. An adaptive version of the coding scheme is also implemented and the results are compared at rates of 0.5 and 1.0 bits per pixel.