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|a Image compression is a large area of research. The objective of image compression is to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form. There are so many problems in the digital grayscale encrypted image transferring over the internet, such as security level of encrypted image, the speed of internet, time of encrypted image transferring and so on. One of these problems is the insufficient of internet bandwidth that the encrypted image will transferred through it, so to solve the problem of insufficiently of internet bandwidth, the grayscale image will compressed by using quadtree fractal compression method before encrypting this image and transferring it via internet. Quadtree fractal compression method has advantage of high compression ratio but also has disadvantage with a long time of compression process which it effected on the decompressed image quality. In this thesis, we focused on quality problem of decompressed decrypted image, it is mean, how to improve quadtree fractal image compression to keep the image quality with reducing in compression time. So to solve this problem, the strength and limitations of current compression scheme has been investigated, design and develop new scheme that improved quality to overcome the limitation, and finally evaluate the new schemes using application scenarios. The proposed scheme improved the image quality by presenting improved quadtree fractal compression algorithm, which change the searching way for the best corresponding domain transformation and ranges, by dividing the image in to 3 selfsimilarity areas. Maximum and medium and minimum self-similarity areas. So the matching process had less time and better quality. The results shows that the proposed improved quadtree fractal compression get the best PSNR 37dB and compression ratio 35.9 and processing time with 65msc
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