Reconstruction, image iterative method

W.C. Chew and Y.M. Wang. Reconstruction of two-dimensional permittivity distribution using the distorted born iterative method. IEEE Transaetions on Medical Imaging, 9, 1990. 

Image Space Reconstruction Algorithm. ISRA (Daube-Witherspoon and MuehUehner, 1986) is a multiplicative and iterative method which yields the constrained maximum likelihood in the case of Gaussian noise. The ISRA solution is obtained using the recursion ... 

The filtered backprojection can be applied to 3D image reconstruction with some manipulations. The 3D data sinograms are considered to consist of a set of 2D parallel projections, and the FBP is applied to these projections by the Fourier method. The iteration methods also can be generally applied to the 3D data. However, the complexity, large volume, and incomplete sampling of the data due to the finite axial length of the scanner are some of the factors that limit the use of the FBP and iterative methods directly in 3D reconstruction. To circumvent these difficulties, a modified method of handling 3D data is commonly used, which is described below. 

When do you apply various corrections (e.g., detection efficiency variations, noise components, random and scatter coincidences, attenuation) in the FBP and iterative methods of image reconstruction ... 

Attenuation correction factors are calculated from the blank transmission scan (Step 12) and patient transmission scan (Step 19). Reconstruct images using the corrected data with appropriate reconstruction algorithms (FBP or iterative method), provided by the manufacturer. 

Attenuation correction factors are applied to acquired PET data (Step 15). PET images are then reconstructed from corrected data using either the FBP or the iterative method depending on the vendor s software. 

A new one-dimensional mierowave imaging approaeh based on suecessive reeonstruetion of dielectrie interfaees is described. The reconstruction is obtained using the complex reflection coefficient data collected over some standard waveguide band. The problem is considered in terms of the optical path length to ensure better convergence of the iterative procedure. Then, the reverse coordinate transformation to the final profile is applied. The method is valid for highly contrasted discontinuous profiles and shows low sensitivity to the practical measurement error. Some numerical examples are presented. 

Figure 7-7 illustrates the focusing inversion result obtained by the re-weighted regularized conjugate gradient method. The plots of the misfit and parametric functionals are shown in the top panel of Figure 7-7. In this case the data fitting after 50 iterations is within 4% nevertheless the inverse image adec uately reconstructs the true model. We can clearly recognize two bodies in this image, and the densities correspond well to the true model.

After the reconstruction, a cross-check should show that the reference reflection is degenerated to a 5-distribution, and there are no negative intensities in the desmeared image. If this is not the case, the found reference peak was broadened not only by imperfect orientation . In this case an iterative trial-and-error method is helpful the peak is proportionally narrowed, until over-desmearing can no longer be detected. The equations mentioned are directly applicable in case of fiber symmetry. If the symmetry of the scattering pattern is lower, the simplification must be reverted to a set of equations in the complete spherical harmonics instead of the Legendre polynomials. 

Figure 4.10. Comparison of filtered backprojection (FBP) and iterative (OSEM) methods with attenuation correction, (a) Lungs, (b) Normal Liver, (c) Liver with tumor, (d) Breast. FBP images with attenuation corrections are noisier than OSEM images with attenuation correction. (Reprinted by permission of Society of Nuclear Medicine from Riddell C et al (2001) Noise reduction in oncology FDG PET images by iterative reconstructions a quantitative assessment. J Nucl Med 42 1316)...

More work is stiU necessary to identify optimal trade-offs between improved image quality and scanning times. Furthermore, an iterative approach to scan protocol development will have to take into consideration methods which can accommodate image reconstruction noise and increased or decreased spatial resolution. 

An alternative method sometimes used in image reconstruction is the iterative technique. In this category of image reconstruction, two techniques will be discussed an algebraic method without statistical estimation and another with statistical estimation (the maximum likelihood estimation technique). 

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