1792 words - 8 pages

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 developing rapidly we concentrated our thesis on the alternate approach method using wavelet methods.

The aim of the thesis flow is described in the following way like Chapter 1 deals with background literature of the project. In Chapter 2 we briefly describe about the literature survey .Chapter 3 deals with experiment analysis and Chapter 4 is the analysis of results by examining the parameters. Finally the conclusion and future work of the present work

1.2 Wavelet transform

Wavelets are the component waves of sounds and images with finite length and are oscillatory in nature. Wavelets are confined in time and frequency domains. In present world, wavelets have found a wide range of application in the field of signal processing such as image reconstruction, noise reduction. Wavelets can be used to reduce the size of an image without affecting the resolution of an image [3].

Wavelet transforms are categorized into discrete wavelet transforms (DWT) and continuous wavelet transforms (CWT). DWT depends on scaling and wavelet functions. The analysis of signal at different scales is done by using the filters of different cut off frequencies. This decomposes the signal into different frequency bands, which are passed through...

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