A Novel Algorithm of Solving the Optimal Slope on Rate-distortion Curve for the Given Rate Budget

Rate-distortion optimization greatly improves the performance of compression coding system so that it pervades all of the source coding from an informationtheoretic standpoint and for the design of practical coding systems. For the case of rate-distortion optimization, Lagrange multiplier method provides the efficient and nearly optimal solution. In this paper, a fast and efficient algorithm is proposed to solve the optimal slope λ＊ of the rate-distortion curve at the given bit budget. Based on Lagrange multiplier method, the presented algorithm find λ＊ using the golden-ratio search. Compared with the Bisection method that only adapts to the system with the dense operational points on the rate-distortion curve, the proposed algorithm can be adapted to the system whether the operational points are populated densely or not. Thus it can be applied to both the wavelet coding system and the video coding standards such as H. 264, where Bisection method can not work well. In particular, the algorithm has been verified on the platform of the quadtree classified and trellis coded quantized （QTCQ） wavelet image compression system and the newest video coding standard H. 264. The experimental results are provided to demonstrate the efficiency of the algorithm. The proposed algorithm can improve the performance. A gain abour 0.6 - 0.7 dB can be achieved with the same rate in H. 264. In addition, it converges as fast as Bisection method, with almost the same ctinplexity.

Rate-distortion optimization greatly improves the performance of compression coding system so that it pervades all of the source coding from an information-theoretic standpoint and for the design of practical coding systems. For the case of rate-distortion optimization,Lagrange multiplier method provides the efficient and nearly optimal solution. In this paper,a fast and efficient algorithm is proposed to solve the optimal slope λ of the rate-distortion curve at the given bit budget. Based on Lagrange multiplier method,the presented algorithm find λ using the golden-ratio search. Compared with the Bisection method that only adapts to the system with the dense operational points on the rate-distortion curve,the proposed algorithm can be adapted to the system whether the operational points are populated densely or not. Thus it can be applied to both the wavelet coding system and the video coding standards such as H.264,where Bisection method can not work well. In particular,the algorithm has been verified on the platform of the quadtree classified and trellis coded quantized (QTCQ) wavelet image compression system and the newest video coding standard H.264. The experimental results are provided to demonstrate the efficiency of the proposed algorithm. The proposed algorithm can improve the coding performance. A gain about 0.6-0.7dB can be achieved with the same rate in H.264. In addition,it converges as fast as Bisection method,with almost the same complexity.