  The design of the optimal inverse discrete cosine transform (IDCT) to
compensate the quantization error is proposed for effective lossy image
compression in this work. The forward and inverse DCTs are designed in pair in
current image/video coding standards without taking the quantization effect
into account. Yet, the distribution of quantized DCT coefficients deviate from
that of original DCT coefficients. This is particularly obvious when the
quality factor of JPEG compressed images is small. To address this problem, we
first use a set of training images to learn the compound effect of forward DCT,
quantization and dequantization in cascade. Then, a new IDCT kernel is learned
to reverse the effect of such a pipeline. Experiments are conducted to
demonstrate that the advantage of the new method, which has a gain of
0.11-0.30dB over the standard JPEG over a wide range of quality factors.
