Novel 2-D MMSE Subpixel-Based Image Down-Sampling

Abstract

Subpixel-based down-sampling is a method that can potentially improve apparent resolution of a down-scaled image on LCD by controlling individual subpixels rather than pixels. However, the increased luminance resolution comes at price of chrominance distortion. A major challenge is to suppress color fringing artifacts while maintaining sharpness. We propose a new subpixel-based down-sampling pattern called diagonal direct subpixel-based down-sampling (DDSD) for which we design a 2-D image reconstruction model. Then, we formulate subpixel-based down-sampling as a MMSE problem and derive the optimal solution called minimum mean square error for subpixel-based down-sampling (MMSE-SD). Unfortunately, straightforward implementation of MMSE-SD is computational intensive. We thus prove that the solution is equivalent to a 2-D linear filter followed by DDSD, which is much simpler. We further reduce computational complexity using a small <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> × <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> filter to approximate the much larger MMSE-SD filter. To compare the performances of pixel and subpixel-based down-sampling methods, we propose two novel objective measures: normalized <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> high frequency energy for apparent luminance sharpness and PSNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U(V)</sub> for chrominance distortion. Simulation results show that both MMSE-SD and MMSE-SD( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> ) can give sharper images compared with conventional down-sampling methods, with little color fringing artifacts.