Image Formation Methods for Dual Energy and Multi-Energy Computed Tomography.
Semerci, Oguz.
2012
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Abstract: In recent
years, a considerable amount of research in the area of computed tomography (CT) has
been directed to the incorporation of the energy dependency of X-ray attenuation into
the reconstruction scheme. Considering energy dependency is crucial in order to
characterize the chemical composition of materials under investigation rather than
simply providing relative attenuation ... read moreimages as is done in conventional tomography. In
this thesis, novel iterative reconstruction techniques for polychromatic dual energy and
multi-energy CT, which incorporate energy dependency in different ways, are proposed.
Dual energy CT uses two different spectra at the source side to obtain energy selective
information, whereas multi-energy employs energy discriminating photon counting
detectors. The proposed dual energy algorithm has an emphasis on detection and
characterization of piecewise constant objects embedded in an unknown, cluttered
background. Physical properties of the objects, specifically the Compton scattering and
photoelectric absorption coefficients, are assumed to be known with some level of
uncertainty. Our approach is based on a level-set representation of the characteristic
function of the object and encompasses a number of regularization techniques for
addressing both the prior information we have concerning the physical properties of the
object as well as fundamental, physics-based limitations associated with our ability to
jointly recover the Compton scattering and photoelectric absorption properties of the
scene. In the absence of an object with appropriate physical properties, our approach
returns a null characteristic function and thus can be viewed as simultaneously solving
the detection and characterization problems. Unlike the vast majority of methods which
define the level set function non-parametrically, (i.e., as a dense set of pixel
values), we define our level set parametrically via radial basis functions (RBF's) and
employ a Gauss-Newton type algorithm for cost minimization. Numerical results show that
the algorithm successfully detects objects of interest, finds their shape and location,
and gives an adequate reconstruction of the background. The development of energy
selective, photon counting X-ray detectors makes possible a wide range of new and
exciting possibilities in the area of multi-energy CT image formation. Under the
assumption of perfect energy resolution, here we propose a tensor based iterative
algorithm that simultaneously reconstructs the X-ray attenuation distribution for each
energy level. We use a multi-dimensional image model rather than a vector representation
in order to develop a novel tensor-based regularizer. Specifically, we model the
multi-spectral unknown as a 3-way tensor where first two dimensions are in space and the
third dimension is in energy. This approach allows for the design of a tensor nuclear
norm regularizer, which like its two dimensional counterpart, is a convex function of
the multi-spectral unknown. Additionally, we introduce a Tikhonov type regularization
method called adaptively weighted L2 (AWL2), which penalizes the weighted quadratic sum
of the differences between neighbouring pixels, where the weights are updated at each
iteration using a multiplicative update formula adapted to edge information. The
solution to the resulting convex optimization problem is obtained using the alternating
direction method of multipliers (ADMM). Simulation results shows that the generalized
tensor nuclear norm can be used as a stand alone regularization technique for the energy
selective (spectral) computed tomography (CT) problem. When combined with total
variation (TV) regularization of AWL2 it enhances the regularization capabilities of
these techniques especially at low energy images where the effects of noise are most
prominent. Moreover, AWL2 provides excellent edge preserving and noise reduction
capabilities with a simple quadratic formula that are superior to TV in the spectral CT
set-up.
Thesis (Ph.D.)--Tufts University, 2012.
Submitted to the Dept. of Electrical Engineering.
Advisor: Eric Miller.
Committee: Brian Tracey, Shuchin Aeron, Misha Kilmer, and Maokun Li.
Keywords: Electrical engineering, and Biomedical engineering.read less - ID:
- z316qc859
- Component ID:
- tufts:22003
- To Cite:
- TARC Citation Guide EndNote
