Image Reconstruction Using Wavelet Transform with Extended Fractional Fourier Transform

Image reconstruction using wavelet transform using extended fraction Fourier transform Chapter 1 Introduction 1 Background: Image reconstruction is a process in which a two-dimensional or three-dimensional image is composed of a projected set of one-dimensional images. It also includes techniques for developing high resolution images from a set of low resolution images. Because MRI or CT data used in the medical field must be visualized in detail, difficulties in the medical field have resulted in image reconstruction at the beginning of the 20th century.

The Fourier transform is a mathematical transformation applied to transform a signal or image from the time domain to the frequency domain, which has many uses. Fourier images convert real values ​​to complex values. Next, for use in various fields, the information is converted from a complex value to an actual value. As the MRI process begins, each proton begins to rotate at a rate (approximately 63 MHz) proportional to the applied magnetic field. As 63 MHz is in the radio frequency range (RF), as RF power is sent to protons, they tend to react. Add an additional magnetic field "gradient". This leads to "R" resonance of MRI. RF moves around the body to shoot various images

The most basic way to extract a texture descriptor from an image is based on a Fourier transform. The initial image is transformed by a Fourier function. Since this method is applicable to digital images, Discrete Fourier Transform (DFT) is used. DFT converts an image from the spatial domain to the frequency domain. The frequency domain represents all the spatial frequencies of the original image. In other words, the converted image shows the intensity change of a plurality of pixels. The converted data is grouped therefrom to obtain multiple metrics. Descriptors are formed from these metrics and used for comparison. (Nixon, 2007)

To reconstruct an image, 1D Fast Fourier Transform (FFT) must be used. Next, according to the Fourier slice theorem, the spectrum of each view is the same as the value of a line (slice) passing through the image spectrum, guaranteeing that each view in the grid has the same angle as it was originally acquired . Finally, reconstruction of the scanned object is achieved using the inverse FFT of the image spectrum. As mentioned earlier (Section 6), the linear damping coefficient gives a rough image of the object. In fact, these can be expressed in dB / cm, but depend on the incident radiant energy, so instead of representing the image using the attenuation coefficient in the CT scan, use an integer called the CT value instead I will. Although they occur occasionally, they are informally called hounsfield units and have the following relationship with the linear damping coefficient.