Recently, many researchers started to question a long-standing paradox in the engineering practice of digital photography: oversampling followed by compression, and pursue more intelligent sparse sampling techniques. In this research we take a practical approach of uniform down sampling in image space, and the sampling is made adaptive by a spatially varying directional low-pass prefiltering. Since the down-sampled prefiltered image is a low-resolution image of conventional square sample grid, it can be compressed and transmitted without any change to current image coding standards and systems. The decoder first decompresses the low-resolution image and then upsamples it to the original resolution by least-square estimation using a 2D piecewise autoregressive model and the knowledge of directional low-pass filter. The proposed joint adaptive down-sampling and up-sampling technique outperforms JPEG 2000 (the state-of-the-art in lossy image coding) in PSNR measure at low to modest bit rates and achieves superior visual quality at all bit rates. This work shows that oversampling not only increases cost and energy consumption, but it could, even when coupled with a sophisticated rate-distortion optimized compression scheme, cause inferior image quality at certain bit rates.