Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform

@article{Luo2014AdjointSM,
  title={Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform},
  author={Songting Luo and Jianliang Qian and Plamen Stefanov},
  journal={SIAM J. Imaging Sci.},
  year={2014},
  volume={7},
  pages={696-715}
}
Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply efficient fast sweeping methods to solve static transport equations and adjoint state equations… 
Algebraic Reconstruction of Source and Attenuation in SPECT Using First Scattering Measurements
Here we present an Algebraic Reconstruction Technique (ART) for solving the identification problem in Single Photon Emission Computed Tomography (SPECT). Traditional reconstruction for SPECT is done
Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data
In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements.
Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data
This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization
Least squares spectral collocation method for solving identification problems in a Lake pollution model over a complex domain
Abstract: In this paper, We modeled the behavior of pollution concentration in a lake by a parabolic equation. The domain of the lake is reduced to 2D-dimension in space and characterized by some
A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations
TLDR
This work presents a fast sweeping method for a class of Hamilton-Jacobi equations that arise from time-independent problems in optimal control theory and displays the utility of the method by applying it to relevant problems from engineering.
Convergence analysis of the fast sweeping method for static convex Hamilton–Jacobi equations
In this work, we study the convergence of an efficient iterative method, the fast sweeping method (FSM), for numerically solving static convex Hamilton–Jacobi equations. First, we show the

References

SHOWING 1-10 OF 40 REFERENCES
The identification problem for the attenuated X-ray transform
We study the problem of recovery both the attenuation $a$ and the source $f$ in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there is a natural
Numerical solution of the identification problem for the attenuated Radon transform
The attenuated Radon transform serves as a mathematical tool for single-photon emission computerized tomography (SPECT). The identification problem for the attenuated Radon transform is to find the
Combined source and attenuation reconstructions in SPECT
We consider the simultaneous reconstruction of the absorption coefficient and the source term in a linear transport equation from available boundary measurements. This problem finds applications in
The inverse problem of emission tomography
The image reconstruction process in emission computed tomography (ECT) is an inverse problem for the photon transport equation. For monochromatic emission sources it is closely related to the
A New Approach to the Emission Computerized Tomography Problem: Simultaneous Calculation of Attenuation and Activity Coefficients
In order to obtain truly quantitative reconstruction of gamma-emitter concentration in Emission Computerized Tomography (ECT) the attenuation within the region of interest has to be accounted for. In
An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals
Abstract : Traditional transmission travel-time tomography hinges on ray tracing techniques. We propose a PDE-based Eulerian approach to travel-time tomography so that we can avoid the cumbersome
A new approach towards simultaneous activity and attenuation reconstruction in emission tomography
In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the
Reconstruction of attenuation map using discrete consistency conditions
  • A. Bronnikov
  • Computer Science
    IEEE Transactions on Medical Imaging
  • 2000
TLDR
A new approach based on the discrete consistency conditions, which can easily be applied in various scanning configurations, including fully three-dimensional (3-D) data acquisition protocols, and provides a stable numerical implementation, allowing one to avoid the crosstalk between the attenuation map and the source function.
Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatially-varying attenuation distribution
  • R. Ramlau, R. Clackdoyle
  • Mathematics
    1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255)
  • 1998
Reports on an iterative approach to reconstruct the activity f(x) directly from the emission sinogram data without additional transmission measurements. The proposed algorithm is based on iterative
The identification problem for the exponential Radon transform
The exponential Radon transform, which arises in single photon emission computed tomography, is defined by ℛ ƒ(μ:ω,s) = ∫Rƒ(sω + tomega;⟂) eμt dtƒ. Here ƒ is a compactly supported distribution in the
...
...