PSNR estimate for JPEG compression

JPEG is wildly used for image compression, which inevitably introduces some distortions, such as blocking artifacts and blurring. Peak Signal to Noise Ratio (PSNR) is the most widely used objective criterion to evaluate image distortion, which is a full reference image quality assessment and requires original image as the reference. However, this requirement cannot always be guaranteed, so that no reference PSNR estimate (NRPE) is required in some applications. NRPE is an ill-pose problem and need some prior knowledge to produce rational results. DCT coefficients are usually assumed with even or Gaussian distributions, and their parameters are estimated by learning or no learning based algorithms in PSNR calculation. These works are unsatisfied for their estimate error is even larger than 3 dB for the heavy compressed images. Note that the correlations of image pixels will be destroyed and some artifacts will appear after heavy compression, such as blocking and blurring. In this paper, the relationship of mean squared difference of slope (MSDS), pixel correlation, image variance and the left alternating current (AC) energy is theoretically analyzed, and then PSNR is constructed as the function of MSDS and left AC energy. The left AC energy cannot be exactly measured in decoded image, hence that it is replaced by the index of the last nonzero coefficients for simplicity. Benefit from this arrangement, the proposed algorithm produces more accurate results over the-state-of-art NRPE algorithms.