A number of novel approaches to image data compression have been proposed, which attempt to compress the image by analysing it into regions of uniform gray level and texture and synthesising an approximation, which is accurate only in a statistical sense, at the receiver. This paper attempts to establish what gains may be achieved by such methods and what the problems are in finding a viable method. The perceptual properties of textures are considered and methods for analysing them and synthesising them are discussed. It is shown that although savings over conventional methods of data compression can be large, there are some difficult problems to overcome in developing a practicable system.