scholarly journals Bayesian Maximum-A-Posteriori Approach with Global and Local Regularization to Image Reconstruction Problem in Medical Emission Tomography

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1108
Author(s):  
Natalya Denisova
Keyword(s):  
Image Reconstruction ◽  
Single Photon ◽  
Photon Emission ◽  
Reconstruction Algorithm ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Local Regularization ◽  
Global And Local ◽  
Prior Models ◽  
Global Regularization

The Bayesian approach Maximum a Posteriori (MAP) provides a common basis for developing statistical methods for solving ill-posed image reconstruction problems. MAP solutions are dependent on a priori model. Approaches developed in literature are based on prior models that describe the properties of the expected image rather than the properties of the studied object. In this paper, such models have been analyzed and it is shown that they lead to global regularization of the solution. Prior models that are based on the properties of the object under study are developed and conditions for local and global regularization are obtained. A new reconstruction algorithm has been developed based on the method of local statistical regularization. Algorithms with global and local regularization were compared in numerical simulations. The simulations were performed close to the real oncologic single photon emission computer tomography (SPECT) study. It is shown that the approach with local regularization produces more accurate images of ‘hot spots’, which is especially important to tumor diagnostics in nuclear oncology.

scholarly journals A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images

Tomography ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 286-300
Author(s):  
Abdelwahhab Boudjelal ◽  
Abderrahim Elmoataz ◽  
Bilal Attallah ◽  
Zoubeida Messali
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Single Photon ◽  
Signal To Noise Ratio ◽  
Practical Importance ◽  
Photon Emission ◽  
Reconstruction Algorithm ◽  
Emission Computed Tomography ◽  
Edge Preserving ◽  
Emission Computed

The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

scholarly journals A geometric based preprocessing for weighted ray transforms with applications in SPECT

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fedor Goncharov
Keyword(s):  
Single Photon ◽  
Photon Emission ◽  
Reconstruction Algorithm ◽  
Emission Computed Tomography ◽  
Radon Transforms ◽  
Single Photon Emission Computed ◽  
Ray Transforms ◽  
Straight Lines ◽  
The Impact ◽  
Photon Emission Computed Tomography

AbstractIn this work we investigate numerically the reconstruction approach proposed in [F. O. Goncharov and R. G. Novikov, An analog of Chang inversion formula for weighted Radon transforms in multidimensions, Eurasian J. Math. Comput. Appl. 4 2016, 2, 23–32] for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a geometric reduction of the data modeled by weighted ray transforms to new data modeled by weighted Radon transforms along two-dimensional planes in 3D. Such reduction could be seen as a preprocessing procedure which could be further completed by any preferred reconstruction algorithm. In a series of numerical tests on modelized and real SPECT (single photon emission computed tomography) data we demonstrate that such procedure can significantly reduce the impact of noise on reconstructions.

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