A new perceptually relevant entropy-constrained coding scheme based on the just-noticeable-distortion (JND) level of the human observer is described and its properties demonstrated. The JND at each pixel location is defined as the threshold of detectability of the human visual system (HVS) to errors in reproducing that pixel. Because of the masking effect of the HVS, errors below the JND are rendered imperceptible. The JND is determined empirically as a function of spatial frequency, local texture and local contrast. A distortion measure is developed, making essential use of the JND, for a subband coding environment which attempts to mimic the subjective evaluation effects of the HVS. This distortion measure employs a weighted squared-error metric, where the weighting depends upon the JND value at each pixel position. It essentially assigns near-zero distortion to subthreshold errors and approximately squared-error distortion to superthreshold errors. This perceptual distortion measure was incorporated into a previously developed design procedure for entropy-constrained subband coding (ECSBC) schemes based upon training data. We demonstrate that, compared to use of the conventional squared-error distortion, significant improvements in subjective image reconstruction quality can be achieved at low average bit rates using this perceptual distortion measure.