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A fundamental theorem in the drift analysis of EAs was initially presented in Jun He and Xin Yao's paper(Artificial Intelligence 127(1) (2001) 57–85). However, the theorem remained defective in spite of its successful applications in some specific cases. This paper points out those defects, then suggests some modifications on the theorem and introduces a new and rigorous proof. This work is expected to contribute to the solid foundation of runtime analysis of Evolutionary Algorithms.

Block-based DCT compression methods usually result in discontinuities called blocking artifacts at the boundaries of blocks due to the coarse quantization of the coefficients. In order to save more computations, an algorithm directly based on DCT-domain is proposed. It reduces the blocking artifacts as much as possible and preserve edge adequately as well. The algorithm presents a specific and convenient edge detection criterion. For the non-edge blocks, one-dimension DCT is used on each row of two adjacent blocks and the shifted block, and then the transform coefficients of the shifted block are replaced by adaptively weighted average of three blocks' coefficients. For the edge blocks, Sigma filter is used to smooth the block boundaries. Simulation results show that the proposed reducing blocking artifacts algorithm outperforms the existing algorithms.