Computer implemented methods of compressing and decompressing image data are described. A discrete cosine (DCT) transformation is applied to each of a plurality of pixel blocks to generate a set of DCT coefficients for each pixel block comprising a DC DCT coefficient and a plurality of AC DCT coefficients. Each set of DCT coefficients is quantised. A DC array is formed from the set of quantised DC DCT coefficients and an AC matrix is formed from the set of quantised AC DCT coefficients. The AC matrix is compressed by eliminating blocks of data having only zero values and forming a reduced AC array from blocks including non-zero values. The reduced AC array is compressed using a key to form a coded AC array. The DC array and coded AC array are arithmetically coded to form arithmetically coded data which is included in a compressed image file. The decompression method is essentially the reverse process
