Different methods of standard definition (SD) to high definition (HD) image conversion
are compared according to the PSNR criterion. Subjective comparison is difficult as
there is almost no quality difference between them. For comparison, an original HD and the
correspondent SD images are required. The SD image is up-converted to approximate HD
images using various methods and then these approximated images are compared to the
original HD image. In such a comparison the main question is how to generate the SD image. Both analytical
and simulation results show that the method of generation of the SD image has a great influence on the outcome
of PSNR results. Immediate down-sampling, Filtered down-sampling, Discrete Fourier Transform
(DFT)-based down-sampling and Discrete Cosine Transform (DCT)-based down-sampling are methods we
used to generate SD image from the original HD image. Ideal low pass signal (Nyquist) interpolation, DFTbased
up-sampling and DCT-based up-sampling are the three methods we used to up-convert SD to HD image.
As it is seen, the highest PSNR (least error) is the mean squared value of the omitted high frequency
components during down-sampling process in transform-based methods. The analytical formulation of PSNR
in filtered-based methods is not simple due to distortions in the frequency response of filters and aliasing in
Keywords: Discrete cosine transform, discrete fourier transform, down-sampling, nyquist rate, PSNR, upsampling.
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