The present invention relates to a method for recovering a compressed image for an image processing technique and an apparatus therefor. In the present invention, a cost function is defined in consideration with a directional characteristic of the pixels which will be recovered and a plurality of pixels of the recovering pixels. In addition, a regularization parameter variable having a certain weight is obtained from the cost function, and the regularization parameter variable is approximated using the compressed pixel for thereby obtaining a recovering pixel. The regularization parameter variable has a weight of a reliability with respect to the original image and a weight of a smoothing degree of the original image. In the methods and apparatuses for recovering a compressed motion picture a cost function is defined in consideration with a directional characteristic of the pixels which will be recovered and a plurality of pixels of the recovering pixels. In addition, a regularization parameter variable having a certain weight is obtained from the cost function, and the regularization parameter variable is approximated using the compressed pixel for thereby obtaining a recovering pixel. In the methods and apparatuses for filtering, a filtering method is selected from filtering methods having different filtering strengths based on whether a pixel being filleted is in an intra-coded portion of an image.