Abstract: A method and apparatus for performing a multi-stage wavelet transform on a block of image data, using a smaller memory than would be required to implement an equivalent conventional multi-stage wavelet transform on the same block, and a method and apparatus for performing compression on a block of image data by performing a multi-stage wavelet transform on the block, quantizing coefficients resulting from the multi-stage wavelet transform, and performing entropy encoding on the quantized coefficients. Typically, the input image data is generated by a document scanner, and is compressed in a manner allowing fast decompression (by employing simple entropy encoding) and imposing low memory requirements.