The degradation in image quality, produced by compression, can be regarded as multidimensional in nature, involving tone, color, sharpness and noise. By measuring each of these categories separately, and then combining to form a single figure of merit or quality metric, a better understanding of the effects of compression on quality can be achieved. This approach is superior to the use of single overall measures of 'quality,' such as the mean squared error (MSE) measurement of distortion. Tone reproduction is assessed using cascaded transfer functions. Color reproduction is assessed using both the CIE (1976) L*a*b* color difference measure and a color metric, the color reproduction index, based on a proven model of color vision. Image sharpness and noise are evaluated using the modulation transfer function (MTF) and the noise power spectrum (NPS) respectively. These results are combined, together with characteristics of the display system and a 'typical' observer, in an image quality metric based on the square root integral (SQRI) metric. Comparisons are made between the various methods of assessment, and objectively measured quality is correlated with results from subjective scaling experiments. Problems with the application of methods based on linear systems analysis are described and possible solutions suggested.