Block-based video-coding standards produce unwanted spatial and temporal artifacts in reconstructed videos. Among them, ringing and mosquito artifacts arise due to the quantization of high-frequency discrete cosine transform coefficients. Most of the existing artifact-reduction algorithms assume that coding information such as a standard quantization table and the corresponding quantization parameter for each block are available. In many multimedia applications, however, external video inputs are usually supplied without coding information. To effectively reduce the ringing and mosquito artifacts in a decoded input video sequence, it is necessary to control the filter strength block by block. In this paper, we present a blind block-based method to estimate the quantization amount and propose a novel post-processing algorithm based on the visibility of artifacts in terms of the human visual system using the estimated quantization amount. Experimental results demonstrate that the proposed algorithm better alleviates ringing and mosquito artifacts in various coded videos compared with the existing algorithms.