1. An image data processing system which includes a video memory for storing the one frame image data and an apparatus for compressing and decompressing the image data for sending and receiving the compressed data through a transmitter and a receiver via a channel, the means for compressing and decompressing the image data comprising: a first block memory for storing the image data from said video memory per predetermined block unit; a block segmentator for dividing said image data provided by said first block memory into prescribed number of sub-blocks in accordance with the shape or complicity of the image; a first switch for changing the data transfer path based on whether the image data provided from said block segmentator is the one that corresponds to the substantially complicated image; a first and second compressors for compressing the image data through said first switch respectively by adopting different compression methods, and for providing the compressed data with said transmitter; an extra information generator for producing an information data that represents whether said divided image data in sub-blocks from said block segmentator was compressed by said first compressor or said second compressor, and for providing the extra information data with said transmitter; a second switch for changing the data transfer path for said compressed image data based on the information of said extra data which are received by said receiver from said transmitter; a first and second decompressors for restoring said compressed image data through said second switch by adopting different decompression methods respectively which are corresponding to said different compression method; a block mixer for composing the predetermined sub-blocks pixels successively provided from said first decompressor or second decompressor to be restored to its original image of said predetermined block unit; and a second block memory for storing said restored original image data of predetermined blocks provided by said block mixer and for writing said restored original image data into said video memory.