Linear programming optimization for video coding under multiple constraints

A linear programming (LP) technique that performs rate-distortion based optimization for constrained video coding is introduced. Given the assumption of piecewise linear and convex rate-distortion functions, LP is used to generate optimal solutions for the minmax problem under VBR buffer constraints. The LP solution for this problem avoids an explicit search for the maximum distortion value. To verify the linearity and convexity assumptions, this minmax optimization procedure is applied to the MPEG-2 framework with macroblock level rate control under VRB buffer constraints. The results show an improvement in average PSNR of approximately 0.5 dB to 2.0 dB over the initial TM5 solution, while maintaining an almost constant PSNR level. As a second LP application, a minimum rate problem with constraints on linear combinations of frame-level distortions is considered. Using the previous assumptions on the rate-distortion functions, it is proven that the LP solution is optimal. The LP technique yields a computationally efficient solution for this filtered distortion problem.