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...
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...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
Tanaka, K., Saito, H. A., Fukada, Y., & Moriya, M. (1991). Coding vidual images of objects
X-rays have benefited the medical field for over a hundred years (Radiology). Wilhelm Conrad Roentgen, a German Physics Professor, discovered the x-ray (Career as a Radiologic Technician, Radiography, Ultrasound X-ray Technician). Dartmouth College in New Hampshire performed the first procedure on February 3, 1896 (Radiology). Radiologic
This approach produces many obvious spurious minutiae in the reconstructed fingerprint, which can be easily detected. The fingerprint reconstruction (from minutiae) approach proposed by Feng et al. [4] takes advantage of the amplitude and frequency modulated (AM-FM) fingerprint model [6], in which the phase image is used to determine the ridges and minutiae. The phase image contains two parts: the continuous phase and the spiral phase (which corresponds to the minutiae). In [4], the authors propose to incorporate a piecewise planar model for the continuous phase reconstruction. This model predicts the continuous phase block by block based on the gradient of the continuous phase. The fingerprint is reconstructed by combining the continuous phase and the spiral phase, which has a good matching against the original fingerprint. However, the reconstructed fingerprint does not match well when compared with different impressions of the original fingerprint. Furthermore, the piecewise planar model introduces blocking affects in the continuous phase and the reconstructed fingerprint. For fingerprint with singularity, additional artifacts may appear in the reconstructed fingerprint due to the discontinuity in the continuous phase. The various applications of minutiae-based fingerprint recognition systems, it is very important to investigate to which extreme a reconstructed fingerprint can be similar to the original fingerprint. So as to prompt the research of counter measures a...
Since the discovery of X-rays in 1895 by Wilhelm Röntgen, radiology has contributed substantially to the medical field. Today, X-rays are still considered to be one of the most important tools in diagnostic imaging. Further advancements in imaging have combined the use of nuclear science and radiography and is known as nuclear medicine.
Dubey, R.B., et al. “The Current CAD and PACS Technologies in Medical Imaging.” International Journal of Applied Engineering Research 4.8 (2009): 1439-1456. Academic Search Complete. Web. 20 Feb. 2011.
Image quality assessment is another step in image processing in which statistical parameters are used to measure the quality of the processed image in reference to the raw image or the original image. We shall discuss that later in Chapter 5.
A computerized Axial tomography scan is medical equipment used to image different regions of a human body as well as other animals with internal health problems. A CAT scan uses the idea of conventional X- ray imaging to a higher standard. Instead of just taking pictures of the different body part of interest, the CAT scan takes multiple pictures of the body at many different angles and creates a three dimensional structure of the body. This three dimensional structures show’s a complete body components starting with the bone, tissues, muscles and even vessels at organ level. This can help doctors examine each slide of skin at a time so that way they can pinpoint specific problem to specific regions and find the right solutions to various problem they encounter.
Functions that can be accomplished during preprocessing include: persistence, which reduces noise and smooths the image by frame averaging; panoramic imaging, where the transducer’s normal field of view is expanded beyond normal limits; and spatial compounding, the averaging of many frames that view the anatomy from different angles. Persistence and spacial compounding help to reduce image noise. “In certain cases… the noise can restrain information which is valuable for the general practitioner” (Sudha, Suresh, Sukanesh, 2009). Figure 3 shows the remarkable improvement to image quality with spacial compounding. The processed scan line signals move on to the scan converter where they are converted into image form. The image plane is divided into pixels representing anatomical locations. In digital memory, the pixels are assigned a number representing a shade of gray that corresponds to the echo strength in that area. When the line data is in the appropriate format, it is available for display, storage, and cineloop review (Miele,
Bushong, S. C. (1997). Radiologic science for technologists: physics, biology, and protection (6th ed.). St. Louis: Mosby- Year Book. Inc.
In the above equation 1 & 2 x_n is the windowed input signal, X_k represents the transformed input signal,Y_n represents inverse transformed input signal, N represents length of the input signal.
...erent methods of JND estimation, and study of DCT, SVD and DWT domain is given. Chapter 3 describes problem identification in existence watermarking techniques. Chapter 4 describe a embedding and extracting process of color image digital watermarking based on hybrid DWT-DCT-SVD technique using Human Visual System Model . Chapter 5 analyses the proposed results, demonstrate that the extracted watermark is imperceptible and robust by calculating PSNR, MSE and correlation between extracted watermarks with original. Furthermore, result demonstrates that our scheme is also resistant to the following attacks: counterfeit, collusion or by adding different noise, and image rotation, while almost all robust watermarking schemes are vulnerable to these attacks. Finally Chapter 6 gives a concluding remark that is specified. Possible extensions and improvements are discussed.
Computers are also used to analyze images taken before surgery. Dr. Ninian Peckitt uses software to analyze a CAT scan images in order to understand his patient’s skull. The program in the computer actually directions for making full size replicas of patients heads.
The purpose of image compression is to represent images with less data in order to save storage costs or transmission time. Without compression, file size is significantly larger, usually several megabytes, but with compression it is possible to reduce file size to 10 percent from the original without noticeable loss in quality. Image compression can be lossless or lossy. Lossless compression means that you are able to reconstruct the exact original data from the compressed data. Image quality is not reduced when using lossless compression. Unlike lossless compression, lossy compression reduces image quality. You can't get the original image back after using lossy compression methods. You will lose some information. [1]
Attenuation is the reduction in the total number of photons remaining in the beam after passing the thickness of the object. This is results of interaction of photons with the object and being absorbed or scattered. As the x-ray beam pass through the patient , the beam will attenuated , and also it depend on part thickness , If the thickness is increased the density of the image will reduced ( ↑ thickness ↑ attenuation ↓ density ). The attenuation is affected by the type of absorber which high atomic number material will have high attenuation (↑ atomic number ↑ attenuation), this is due to the electrons of material interact with the photons (bone high interact with the photons because it composed of calcium).
Bushong, S. C. (2008). Radiologic science for technologists: Physics (9th ed.). St. Louis, MO: Mosby, Elsevier.