Wavelet video coding with dependent optimization

We present a new wavelet video coding algorithm and an optimization framework that allocates bits efficiently among consecutive frames at the pixel level. The video residual coder is based on set partitioning in hierarchical trees and wavelet blocks, allowing flexible bit allocation among active and inactive regions in a video frame. To optimize the encoder for efficient bit allocation, we use Lagrangian methods. First, the rate-distortion cost for each wavelet block is minimized, effectively enforcing the equal-slope rule at the pixel level. The Lagrangian method is then extended to successive frames, and an iterative algorithm is presented to solve the dependent coding problem. Finally, motion search is jointly optimized by including motion vectors in the cost function, completing an optimization framework that enforces the equal-slope rule for all bits at the macroblock level and pixels across consecutive frames. The result is a video compression algorithm that requires no training, no explicit quantization, no floating-point operation for INTER frames, no entropy coding, and allows precise rate control. Compared with the discrete cosine transform code in H.263, the new video coding algorithm has faster decoding procedures and achieves an improvement up to 1.12 dB in a PSNR or 20.6% in bit rate savings for typical sequences used in the video compression community.