Most of the specimens for high-resolution electron microscopy have amorphous surface layers due to contamination during observation and/or damaged surface layers during specimen preparation. Moreover, many specimens are radiation sensitive, and a part of the specimen easily becomes amorphous during the observation. These amorphous materials make clear observation of crystal structure difficult. A periodic structure may be extracted by simply using a periodic mask in Fourier space. However, this kind of mask often introduces a periodic feature in addition to the crystal structure. To reduce such artifacts a Wiener filter or an average background subtraction filter has been discussed. However, these filters do not work for non-ideal crystals, such as cylindrical crystals and nano-crystals, where a translational periodicity is limited to the order of nano-meter. In this report we improve these filters by introducing new ways to estimate a contribution from the amorphous materials.