High-end PC monitors and TVs continue to increase their native display resolution to 4k by 2k and beyond. Subsequently, uncompressed pixel amplitude processing becomes costly not only when transmitting over cable or wireless communication channels, but also when processing with array processor architectures. This paper follows a series of papers we presented earlier on a 4*4 block-based memory compression architecture for text, graphics, and video using a multi-dimensional vector representation with context sensitive control of visually noticeable artifacts. A key feature in the system is the sorting by magnitude of pixel amplitudes. To increase the compression ratio and simultaneously alleviate the limitation on block size, we analyze to which extent the sorting orders can be predicted and we consequently propose new schemes to transmit them efficiently. Depending on the compression ratio, the new cost function defined can be considered as a no-reference or reduced-reference ranking naturalness criterion. We show how pertinent our approach is to additionally correct specific visually noticeable compression artefacts thanks to its adaptive pixel positioning mechanism. Finally, we also provide hints on how to extend this new philosophy to support the optimization of future scalable architectures for transcoding or rendering on high quality displays.