Statistical inverse discrete cosine transforms for image compression

The Discrete Cosine Transform (DCT) has been applied to image and image sequence compression to decorrelate the picture data before quantization. This decorrelation results in many of the quantized transform coefficients equaling zero, hence the compression gain. For the decoder, the very few, sparsely populated, non-zero transform coefficient can be utilized for great speed-up in the inverse DCT. This paper describes and compares two styles of implementations of fast inverse DCTs for sparse data. The first implementation that we call the symmetric mapped inverse DCT is based on the forward mapped inverse DCT, but our implementation is up to three times faster. The second implementation is based on a scaled inverse DCT, with detection of zero values. Both implementations are tested for speed against other algorithms, under varying degrees of DCT coefficient sparseness.