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Contributed Talks

Victoria M. Márquez (Universidad de Sevilla): Iterative algorithms for nonexpansive mappings with
    applications to the split feasibility problem. (abstract)

Many practical problems can be formulated as a fixed point problem

x = T x

where T is a nonexpansive mapping defined on a closed convex subset C of a Hilbert space X. That is the case of the Split Feasibility Problem (SFP), introduced by Censor and Elfving in 1994:

Find a point x* such that x*∈C and Ax*∈Q,

where C and Q are closed convex subsets of Hilbert spaces H₁ and H₂, respectively, and A: H₁→H₂ is a bounded linear operator. Some problems in signal processing, such as phase retrieval and design of a nonlinear synthetic discriminant filter for optical pattern recognition, can be formulated as the SFP.

The SFP can equivalently be rewritten as a fixed point problem

 x* = Tx* := P_C ( I - γ A* ( I - P_Q ) A ) x*

where P_C and P_Q are the (nearest point) projections onto C and Q, respectively, γ is any positive parameter, and A* is the adjoint of A. The computation of the projection operator is not always easy, due to the fact that it may lack to have a closed form. But it is known that for sufficiently small γ>0 the mapping T = P_C ( I - γ A* ( I - P_Q ) A ) is nonexpansive, so to avoid these possible difficulties, we present a general perturbation technique for approximating a fixed point of a nonexpansive mapping. We will see how this technique can be applied to the more general form of the SFP called Multiple-set Split Feasibilty Problem.

Scott N. Penfold (University of Wollongong): Block-iterative and string-averaging projection algorithms
    in proton computed tomography image reconstruction. (abstract)

Proton computed tomography (pCT) is a novel imaging modality that has been suggested as a means for maximizing the potential benefits of proton radiation therapy. Proton CT is based on individual proton tracking. The position and direction of protons pre and post patient, as well as the energy lost by the proton in the imaging volume is recorded in list-mode. By measuring the energy lost, the integral relative electron density along the proton path can be calculated. Proton-by-proton tracking is necessary due to the effects of multiple Coulomb scattering (MCS), a process that deviates the proton path from a straight line. If optimal spatial resolution is to be achieved, the path of each proton must be predicted with a maximum likelihood formalism that models MCS. Further, image reconstruction methods are required that are able to handle these non-linear paths. This has led to the exploration of algebraic reconstruction techniques (ART) in pCT. However, because iterative algebraic methods are computationally expensive, parallel compatible versions of the ART class, executed simultaneously over multiple processing units are required if pCT is to be realistic for a clinical environment. In this study we investigate the image quality achievable with block-iterative and string-averaging projection algorithms in application to simulated pCT data. From the results we make a recommendation as to which algorithms should be used in future studies with pCT image reconstruction.

Gangrong Qu (Beijing Jiaotong University): Landweber schemes for linear system in Hilbert space.
    (abstract)

We study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition (SVD) for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions and accelerated strategies. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X-ray tomography, extrapolation of band-limited functions, and angle-limited image reconstruction.

Vadim Soloviev (University College London): 3D fluorescence lifetime imaging in turbid
    inhomogeneous media by using time-gated data acquisition. (abstract)

We present a novel algorithm for simultaneous reconstruction of optical parameters, quantum yield and lifetime in turbid media with embedded fluorescent inclusions. This algorithm is designed in the Fourier domain as an iterative solution of a system of differential equations of the Helmholtz type and does not involve full ill-conditioned matrix computations. The approach is based on allowing the unknown optical parameters, quantum yield and lifetime to depend on the Fourier spectral parameter. The algorithm was applied to time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Relatively accurate reconstruction demonstrates the potential of the method.

Lei Zhu (Stanford University): Scatter correction for x-ray conebeam CT using one-dimensional primary
    modulation. (abstract)

Scatter is considered as one of the fundamental limitations of cone-beam CT (CBCT) image quality. Recently, we developed an efficient scatter correction method for x-ray imaging using primary modulation. A two-dimensional (2D) primary modulator with spatially variant attenuating materials is inserted between the x-ray source and the object to separate primary and scatter signals in the Fourier domain. Due to the high modulation frequency in both directions, the 2D primary modulator has a strong scatter correction capability for objects with arbitrary geometries. However, signal processing on the modulated projection data requires knowledge of the modulator position and attenuation. In practical systems, mainly due to system gantry vibration and the ramp-filtering in the reconstruction, the insertion of the 2D primary modulator results in artifacts such as rings in the CT images, if no post-processing is applied. In this work, we eliminate the source of artifacts in the primary modulation method by using a one-dimensional (1D) modulator. The modulator is aligned parallel to the ramp-filtering direction to avoid error magnification, while sufficient primary modulation is still achieved for scatter correction on a quasi-cylindrical object, such as a human body. The scatter correction algorithm is also greatly simplified for the convenience and stability in practical implementations. The method is evaluated on a clinical CBCT system using the Catphan@600 phantom. The result shows effective scatter suppression without introducing additional artifacts. In the selected regions of interests, the reconstruction error is reduced from 187.2HU to 10.0HU if the proposed method is used.

                                    a)                                                                            b)

Figure. a) 1D comparison of the estimated scatter and the measured scatter using a fan-beam geometry; b) 1D comparison of the line integral profiles without scatter correction, with scatter corrected using the proposed method and with scatter suppressed using a fan-beam geometry.

 

 

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Note:

• The slots for Contributed Talks are limited. Please submit your abstract as soon as possible. Late submissions may not be included in the program, but can be presented as posters.




• This list is partial and is being updated until the start of the conference.




• For the complete list of invited talks click here.

 

Copyright © 2007
by
Image Research Lab, School of Mathematical Sciences, Peking University
Center for Computational Mathematics and Scientific Computation, University of Haifa
Biomedical Imaging Division, School of Biomedical Engineering & Sciences at the Virginia Polytechnic Institute and State University