A system includes an encoder configured to compress media objects using a compression loop that includes a residual decomposition component that decomposes a residual signal for a block of the media object being compressed into multiple sub-error signals. The encoder is further configured to enable different transformation and/or quantization processes to be specified to be applied to different ones of the sub-errors. A corresponding decoder is configured to apply inverse transformation/quantization processing to the sub-error signals, based on the transformation/quantization processes that were applied at the encoder. The decoder then re-creates a residual signal from the processed sub-error signals and uses the re-created residual signal to correct predicted values at the decoder.