This invention provides a novel single-pass and multi-pass synchronized 
encoder and decoder, performing order(s) of magnitude faster 
data compression and decompression, at any 
compression ratio with the higher or the same perceived and measured decompressed 
image quality in comparison with the best state-of-the-art compression methods, using order(s) of magnitude less 
system resources (processor complexity, memory size, consumed power, 
bus bandwith, 
data latency). These features are achieved using novel direct and inverse non-stationary filters for the recusive 
octave direct and inverse subband transformation, novel simple context modeling and symbol 
probability estimation using a minimum number of histograms with the fast 
adaptation for the sign and the magnitude of the transformation coefficients, a novel accelerated range coder without division operations, and a novel synchronisation of the compressed data.