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 motionadaptive linear measurements. Further, the decay of normalized absolute coefficients is faster than that of motion-adaptive linear measurements.