This paper examines the properties of Number Theoretic Transforms over FFT. The aim of this study is to show that Number Theoretic Transforms (NTTs) can be really beneficial in terms of error free and faster computation. One and two dimensional NTTs are implemented in MATLAB and properties are verified and as an example convolution is implemented using Fermat number transform(FNT) which is a variant of NTT.A study of comparison of NTT to FFT proves that NTTs are really beneficial in terms of computational complexity and error free computation.
As Image size need to be reduced for the purpose of data storage and transmission for better utilization of the Bandwidth, Images are compressed using lossy and Lossless compression schemes. In this paper Fractal Image Compression, a lossy compression technique is being implemented on medical Images .Fractal Encoding involves partitioning the images into Range Blocks and Domain Blocks and each Range Block is mapped onto the Domain Blocks by using contractive transforms called the Affine Transforms. The Fractal encoding technique takes a longer encoding time and less decoding time. In the present paper Fractal Image Compression using quad-tree Partitioning technique is being implemented. on Medical Images like CT Of Bone and MR Images of Brain The Performance measures like Compression Ratio (CR), Peak Signal To Noise Ratio (PSNR), Mean Square Error (MSE), Encoding time and Decoding Time are determined for the Range Blocks of Sizes 2x2 and 4x4 respectively with different Threshold Values. Mat lab simulated results for these Performance Measures shows that for larger Range Block size, the PSNR Value decreases and CR increases for different threshold Values.
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