Image reconstruction using wavelet transform with extended split Fourier transformChapter1Introduction1.1 Background: Image reconstruction is the process by which, in 2D or 3D, images are constructed from a set of 1D projections of an image. It also includes the technique of developing a high resolution image from a set of low resolution images. Difficulties in the medical field gave rise to image reconstruction in the early 20th century since MRI or CT data used in the medical field must be viewed in detail. The era of image reconstruction began before the advent of the digital camera which can be used to take high resolution images. The mathematical foundations of these reconstruction methods are the Radon transform, the inverse Radon transform (Hoilund 2007) and the projection slice theorem. Computational techniques include filtered back projection and various iterative methods. Several projection geometries are commonly used, including parallel beam, fan beam, and cone beam. The first method was proposed by Johan Radon in 1917 in which the image is created based on the scattering data associated with cross-sectional scans of an object [1]. Several methods of lesser or equal importance have been developed based on the Radon transform over time. In 1972, the first x-ray computed tomography (CT) scan was developed by Godfrey Hounsfield and was used in the field of medicine. The classic reconstruction method is “back projection” [2] which is solely based on the Radon transform. Alternative approaches include Fourier transform and iterative series expansion methods, statistical estimation methods, and wavelet resolution methods. Since wavelet transforms have the advantage over their Fourier counterparts and have been...... middle of paper ...... n secure to DES [7] AlgorithmREFERENCES:[1]. http://people.csail.mit.edu/bkph/other/Radon_English_1917.pdf[2]. http://labs.seas.wustl.edu/bme/wang/epub/2005MX-PRE-Universal.pdf[3].James S. Walker, “An Introduction to Wavelets and Their Scientific Applications,” 2nd ed., 2008 [4]. http://users.rowan.edu/~polikar/WAVELETS/WTpart4.html[5]. Sandeep, Gaganpreet, Dr. Dheerendra Singh, “Comparative Analysis of Haar and Coiflet Wavelets Using Discrete Wavelet Transform in Digital Image Compression”, 2013 Vol. 3, number 3, pp.669-673[6]. I.Samil Yetik, M. Alper Kutay, Haldum M.Ozaktas, “The split Fourier transform and its applications to image representation and beamforming”, 2003