A l1-norm preserving motion-compensated transform for sparse approximation of image sequences

This paper discusses an adaptive non-linear transform for image sequences that aims to generate a l₁-norm preserving sparse approximation for efficient coding. Most sparse approximation problems employ a linear model where images are represented by a basis and a sparse set of coefficients. In this work, however, we consider image sequences where linear measurements are of limited use due to motion. We present a motion-adaptive non-linear transform for a group of pictures that outputs common and detail coefficients and that minimizes the l₁ norm of the detail coefficients while preserving the overall l₁ norm. We demonstrate that we can achieve a smaller l₁ norm of the detail coefficients when compared to that of motion-adaptive linear measurements. Further, the decay of normalized absolute coefficients is faster than that of motion-adaptive linear measurements.