  Good quality video coding for low bit-rate applications is important for
transmission over narrow-bandwidth channels and for storage with limited memory
capacity. In this work, we develop a previous analysis for image compression at
low bit-rates to adapt it to video signals. Improving compression using
down-scaling in the spatial and temporal dimensions is examined. We show, both
theoretically and experimentally, that at low bit-rates, we benefit from
applying spatio-temporal scaling. The proposed method includes down-scaling
before the compression and a corresponding up-scaling afterwards, while the
codec itself is left unmodified. We propose analytic models for low bit-rate
compression and spatio-temporal scaling operations. Specifically, we use
theoretic models of motion-compensated prediction of available and absent
frames as in coding and frame-rate up-conversion (FRUC) applications,
respectively. The proposed models are designed for multi-resolution analysis.
In addition, we formulate a bit-allocation procedure and propose a method for
estimating good down-scaling factors of a given video based on its second-order
statistics and the given bit-budget. We validate our model with experimental
results of H.264 compression.
