摘要:
A method for statistically reconstructing images from a plurality of transmission measurements having energy diversity and image reconstructor apparatus utilizing the method are provided. A statistical (maximum-likelihood) method for dual-energy X-ray CT accommodates a wide variety of potential system configurations and measurement noise models. Regularized methods (such as penalized-likelihood or Bayesian estimations) are straightforward extensions. One version of the algorithm monotonically decreases the negative log-likelihood cost function each iteration. An ordered-subsets variation of the algorithm provides a fast and practical version. The method and apparatus provide material characterization and quantitatively accurate CT values in a variety of applications. The method and apparatus provide improved noise/dose properties.
摘要:
A method is provided for iteratively reconstructing an image of an object. The method includes accessing measurement data associated with the image, and using a simultaneous algorithm to reconstruct the image. Using the simultaneous algorithm to reconstruct the image includes determining a scaling factor that is voxel-dependent, and applying the voxel-dependent scaling factor to a gradient of an objective function to reconstruct the image.
摘要:
A method is provided for reconstructing an image of an object that includes image elements. The method includes accessing measurement data associated with the image elements, introducing an auxiliary variable to transform an original problem of reconstructing the image to a constrained optimization problem, and solving the constrained optimization problem using a method of multipliers to create a sequence of sub-problems and solve the sequence of sub-problems. Solving the sequence of sub-problems includes reconstructing the image by optimizing a first objective function. The first objective function is optimized by iteratively solving a nested sequence of approximate optimization problems. An inner loop iteratively optimizes a second objective function approximating the first objective function. An outer loop utilizes the solution of the second objective function to optimize the first objective function.
摘要:
Methods provided for forward and back-projection, which are referred to as separable footprint (SF) projectors: exemplified by the SF-TR and SF-TT projectors. These methods approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. In some embodiments, the SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction. In some embodiments, the SF-TT projector uses trapezoid functions in both the axial and transaxial directions. Simulations and experiments showed that both SF projector methods are more accurate than conventional distance-driven (DD) projectors. Moreover, the SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. In some embodiments, the SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.
摘要:
A method is provided for iteratively reconstructing an image of an object. The method includes accessing measurement data associated with the image, and using a simultaneous algorithm to reconstruct the image. Using the simultaneous algorithm to reconstruct the image includes determining a scaling factor that is voxel-dependent, and applying the voxel-dependent scaling factor to a gradient of an objective function to reconstruct the image.
摘要:
A method for statistically reconstructing an X-ray computed tomography image produced by a single X-ray CT scan having a polyenergetic source spectrum and an image reconstructor which utilize a convergent statistical algorithm which explicitly accounts for the polyenergetic source spectrum are provided. First and second related statistical iterative methods for CT reconstruction based on a Poisson statistical model are described. Both methods are accelerated by the use of ordered subsets, which replace sums over the angular index of a sinogram with a series of sums over angular subsets of the sinogram. The first method is generalized to model the more realistic case of polyenergetic computed tomography (CT). The second method eliminates beam hardening artifacts seen when filtered back projection (FBP) is used without post-processing correction. The methods are superior to FBP reconstruction in terms of noise reduction. The method and image reconstructor of the invention are effective in producing corrected images that do not suffer from beam hardening effects.
摘要:
Methods provided for forward and back-projection, which are referred to as separable footprint (SF) projectors: exemplified by the SF-TR and SF-TT projectors. These methods approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. In some embodiments, the SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction. In some embodiments, the SF-TT projector uses trapezoid functions in both the axial and transaxial directions. Simulations and experiments showed that both SF projector methods are more accurate than conventional distance-driven (DD) projectors. Moreover, the SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. In some embodiments, the SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.
摘要:
A method is provided for reconstructing an image of an object that includes image elements. The method includes accessing measurement data associated with the image elements, introducing an auxiliary variable to transform an original problem of reconstructing the image to a constrained optimization problem, and solving the constrained optimization problem using a method of multipliers to create a sequence of sub-problems and solve the sequence of sub-problems. Solving the sequence of sub-problems includes reconstructing the image by optimizing a first objective function. The first objective function is optimized by iteratively solving a nested sequence of approximate optimization problems. An inner loop iteratively optimizes a second objective function approximating the first objective function. An outer loop utilizes the solution of the second objective function to optimize the first objective function.