Image Reconstruction Using Wavelet Transform with Extended Fractional Fourier Transform
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 …show more content…
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 .
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 the series of high pass and low pass filters to analyse the high frequencies and low frequencies. CWT is a correlation between a wavelet and signal at different scales, where scale is used to measure of similarity .
In this thesis, we will focus on 3 kinds of wavelets namely Haar wavelet, Daubechies wavelet and Coiflets wavelet.
1.3 Haar wavelet