Mixed noise removal is a major problem in image processing. Different noises have different properties and it is required to use an appropriate removal method for each noise. Therefore, removal of mixed noise needs the combination of removal algorithms for each contained noise. We aim at the removal of the mixed noise composed of Additive White Gaussian Noise (AWGN) and Random-Valued Impulse Noise (RVIN). Many conventional methods cannot remove the mixed noise effectively and may lose image details. In this paper, we propose a new mixed noise removal method utilizing Direction Weighted Median filter (DWM filter) and Block Matching and 3D filtering method (BM3D). Although the combination of the DWM filter for RVIN and BM3D for AWGN removes almost all the mixed noise, it still loses some image details. We find the cause in the miss-detection of the image details as RVIN and solve the problem by re-detection with the difference of an input noisy image and the output by the combination. The re-detection process removes only salient noise which BM3D cannot remove and therefore preserves image details. These processes lead to the high performance removal of the mixed noise while preserving image details. Experimental results show our method obtains denoised images with clearer edges and textures than conventional methods.