We present blind noise strength estimation for removing blocking artifacts associated with block-based compression schemes. The proposed framework is based on edge statistics residing across two neighboring blocks. First, the block boundary discontinuity is statistically analyzed. Next, the discontinuity is approximated by a simple model, and then filtered by controlling a filter strength according to the contents of the blocks. The main advantages of the proposed algorithm are that 1. it is a blind noise estimator without any prior information, 2. it models a noise with the combination of block discontinuity and simple noise-shape components, and 3. it adjusts the strength of a filter adaptively for removing the given noise. To evaluate the proposed scheme, several baseline approaches are described and compared in terms of peak signal-to-noise ratio and a quality metric.