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Recently, the opportunity to treat still images has increased, and a lot of devices such as laptop displays and digital cameras have been developed, therefore, a large amount of data is stored and is transmitted after a compression. One of the most famous international standards for still image compression is JPEG, in which the DCT (Discrete Cosine Transform) is processed and the DCT coefficients are quantized in each DCT block, so that reconstructed images include the blocky noise and the mosquito noise. Therefore, we propose a new method for reducing the blocky noise and the mosquito noise using total variation minimization approach. In the proposed method, by using the total variation filter, an image is decomposed to a skeleton component, which consists of smooth luminance and edges, and a texture component, which consists of small signals and noise. The Sobel filter is used for edge detection from the skeleton component, and the texture component corresponding to around the edges are filtered by using the Median filter. As a result, the blocky noise and mosquito noise in the reconstructed images are reduced, and fine images are obtained.