A method of data compression, for example for images or audio signals, comprises encoding the data using a transform such as a wavelet transform or a DCT, grouping the transform coefficients by most significant bit, and/or bit value, and transmitting them group by group. Where the transform uses a code book, such as matching pursuits, the coefficients may further be grouped by code book value. In one embodiment, the method allows the data to be described entirely by the positions of the coefficients, and the groupings, without any need to store or transmit any coefficient value information whatsoever.