Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography

Cierniak, Robert; Lorent, Anna

doi:10.1016/j.compmedimag.2016.04.001

Cited by 9 publications

(9 citation statements)

References 18 publications

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“…Because it is a very much less computationally demanding approach, by using FFT, we make our reconstruction method independent of the dimensions of the reconstructed image, to an acceptable degree. This approach also outperforms the D-D method regarding the better condition number at the level of problem formulation [11]. This makes our method more competitive in terms of its resistance to the influence of noise and errors in the forward model, and it opens up a new perspective for the regularization of the reconstruction problem.…”

Section: Introductionmentioning

confidence: 84%

“…However, results obtained earlier (see e.g. [11]) show that the reconstruction problem (31) is better conditioned than methods based on the D-D model. In any case, it needs to be regularized in some way, often by the introduction of an additional regularization term.…”

Section: Iterative Reconstruction Proceduresmentioning

confidence: 90%

“…Although there have been attempts to decrease the calculation complex-ity of this approach, as presented, for example, in the paper [10], they have, as yet, only met with limited results. Moreover, this system uses a reconstruction problem model that has been shown to be extremely ill-conditioned [11]. Therefore, there is still room for improvement in such systems.…”

Section: Introductionmentioning

confidence: 99%

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A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

Cierniak

Pluta

Kaźmierczak

2020

Journal of Artificial Intelligence and Soft Computing Research

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The paper presented here describes a new practical approach to the reconstruction problem applied to 3D spiral x-ray tomography. The concept we propose is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This original reconstruction method is formulated taking into consideration the statistical properties of signals obtained by the 3D geometry of a CT scanner. It belongs to the class of nutating reconstruction methods and is based on the advanced single slice rebinning (ASSR) methodology. The concept shown here significantly improves the quality of the images obtained after reconstruction and decreases the complexity of the reconstruction problem in comparison with other approaches. Computer simulations have been performed, which prove that the reconstruction algorithm described here does indeed significantly outperforms conventional analytical methods in the quality of the images obtained.

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Section: Introductionmentioning

confidence: 84%

Section: Iterative Reconstruction Proceduresmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

Cierniak

Pluta

Kaźmierczak

2020

Journal of Artificial Intelligence and Soft Computing Research

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“…The presence of a shift-invariant system in the optimization problem (4) implies that this system is much better conditioned than the least squares problems present in the referential approach [9]. The conception presented above is a full 3D iterative reconstruction algorithm for spiral cone-beam scanner geometry.…”

Section: Statistical Reconstruction Algorithmmentioning

confidence: 99%

Statistical Iterative Reconstruction Algorithm Based on a Continuous-to-Continuous Model Formulated for Spiral Cone-Beam CT

Cierniak

Pluta

2020

Lecture Notes in Computer Science

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This paper is closely related to the originally formulated 3D statistical model-based iterative reconstruction algorithm for spiral cone-beam x-ray tomography. The concept proposed here is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This algorithm significantly improves the quality of the subsequently reconstructed images, so allowing a reduction in the x-ray dose absorbed by a patient. This form of reconstruction problem permits a reduction in the computational complexity in comparison with other model-based iterative approaches. Computer simulations have shown that the reconstruction method presented here outperforms standard FDK methods with regard to the image quality obtained and can be competitive in terms of time of calculation.

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“…The image formation in CT imaging systems is based on the interaction of X-ray photons with different materials. 1 On the other hand, the contrast mechanism of the CT images is based on material attenuation coefficients. 2 Although each material has a unique attenuation coefficient, sometimes in common single-energy CT scans, the constituent materials of the object – despite different atomic number and different chemical structure – are viewed as the same material.…”

Section: Introductionmentioning

confidence: 99%

Quantification of contrast agent materials using a new image- domain multi material decomposition algorithm based on dual energy CT

Mirzaei

Faghihi

2019

BJR|Open

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Objective: Dual-Energy CT (DECT) is an imaging modality in which the objects are scanned by two different energy spectra. Using these two measurements, two type of materials can be separated and density image pairs can be generated as well. Decomposing more than two materials is necessary in both clinical and industrial CT applications. Methods: In our MMD, barycentric coordinates were chosen using an innovative local clustering method. Local clustering increases precision in the barycentric coordinates assignment by decreasing search domain. Therefore the algorithm can be run in parallel. For optimizing coordinates selection, a fast bi-directional Hausdorff distance measurement is used. To deal with the significant obstacle of noise, we used Doubly Local Wiener Filter Directional Window (DLWFDW) algorithm. Results: Briefly, the proposed algorithm separates blood and fat ROIs with errors of less than 2 and 9 % respectively on the clinical images. Also, the ability to decompose different materials with different concentrations is evaluated employing the phantom data. The highest accuracy obtained in separating different materials with different concentrations was 93 % (for calcium plaque) and 97.1 % (for iodine contrast agent) respectively. The obtained results discussed in detail in the following results section. Conclusion: In this study, we propose a new material decomposition algorithm. It improves the MMD work flow by employing tools which are easy to implement. Furthermore, in this study, an effort has been made to turn the MMD algorithm into a semi-automatic algorithm by employing clustering concept in material coordinate’s assignment. The performance of the proposed method is comparable to existing methods from qualitative and quantitative aspects. Advances in knowledge: All decomposition methods have their own specific problems. Image- domain decomposition also has barriers and problems, including the need for a predetermined table for the separation of different materials with specified coordinates. In the present study, it attempts to solve this problem by using clustering methods and relying on the intervals between different materials in the attenuation domain.

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Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography

Cited by 9 publications

References 18 publications

A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

Statistical Iterative Reconstruction Algorithm Based on a Continuous-to-Continuous Model Formulated for Spiral Cone-Beam CT

Quantification of contrast agent materials using a new image- domain multi material decomposition algorithm based on dual energy CT

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