Down–Sampling for Better Transform Compression

The most popular lossy image compression method used on the Internet is the JPEG standard. JPEG’s good compression performance and low computational and memory complexity make it an attractive method for natural image compression. Nevertheless, as we go to low bit rates that imply lower quality, JPEG introduces disturbing artifacts. It is known that at low bit rates a down–sampled image when JPEG compressed visually beats the high resolution image compressed via JPEG to be represented with the same number of bits. Motivated by this idea, we show how down–sampling an image to a low resolution, then using JPEG at the lower resolution, and subsequently interpolating the result to the original resolution can improve the overall PSNR performance of the compression process. We give an analytical model and a numerical analysis of the down–sampling, compression and up–sampling process, that makes explicit the possible quality/compression trade-offs. We show that the image auto-correlation can provide good estimate for establishing the down–sampling factor that achieves optimal performance. Given a specific budget of bits, we determine the down sampling factor necessary to get the best possible recovered image in terms of PSNR.