Image Reconstruction Using Wavelet Transform with Extended Fractional Fourier Transform

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Image Reconstruction Using Wavelet Transform with Extended Fractional Fourier Transform
Chapter1
Introduction
1.1 Background:
Image reconstruction is the process where in 2D or 3D images are constructed from 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. The difficulties in the field of medicine gave birth to image reconstruction in early 20th century since the MRI or CT data used in field of medicine must be visualized in detail. The era of image reconstruction started before the advent of digital camera which can be used to take high resolution images.
The mathematical foundation for 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 a variety of 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 prominence were developed based on the Radon Transform over the course of time. In 1972 the first X ray computed tomography (CT) was developed by Godfrey Hounsfield that served in the field of medicine. The classical method of reconstruction is ‘Back projection’ [2] which is solely based on Radon transform. The alternate approaches include Fourier Transform and Iterative series expansion methods, Statistical Estimation methods and wavelet resolution methods.
Since wavelet transforms have the edge over its Fourier counterparts and have been...

... middle of paper ...

...n to security of DES [7].
The DES encryption and decryption principles [8] are shown in fig below.
Plain text m m c=DES (m,k)
64 bits 64 bits
Key k 64 bits
Cipher text c m
Key k
Fig1.2: DES Encryption and Decryption Algorithm
REFERENCES:
[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, “A Primer on 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,Issue 3,pp.669-673
[6]. I.Samil Yetik, M. Alper Kutay, Haldum M.Ozaktas, “The Fractional Fourier Transform and Its Applications to Image Representation and Beamforming”, 2003

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