Efficient Hyper-Parameter Selection in Total Variation-Penalised XCT Reconstruction Using Freund and Shapire’s Hedge Approach

Chrétien, Stéphane; Lohvithee, Manasavee; Sun, Wenjuan; Soleimani, Masoud

doi:10.3390/math8040493

Cited by 5 publications

(10 citation statements)

References 36 publications

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“…Tables 2 and 3 summarise the numerical values of MSE, PSNR, SSIM computed for each test, that is, using different undersampling rates and masks, for our two different test samples (grape or fish eye retina). The parameter λ was chosen using the simple and efficient method proposed in [60]. As expected the error decreases as a function of the percentage of observed pixels.…”

Section: Performance Resultsmentioning

confidence: 76%

Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

2020

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Reconstruction of 3D objects in various tomographic measurements is an important problem which can be naturally addressed within the mathematical framework of 3D tensors. In Optical Coherence Tomography, the reconstruction problem can be recast as a tensor completion problem. Following the seminal work of Candès et al., the approach followed in the present work is based on the assumption that the rank of the object to be reconstructed is naturally small, and we leverage this property by using a nuclear norm-type penalisation. In this paper, a detailed study of nuclear norm penalised reconstruction using the tubal Singular Value Decomposition of Kilmer et al. is proposed. In particular, we introduce a new, efficiently computable definition of the nuclear norm in the Kilmer et al. framework. We then present a theoretical analysis, which extends previous results by Koltchinskii Lounici and Tsybakov. Finally, this nuclear norm penalised reconstruction method is applied to real data reconstruction experiments in Optical Coherence Tomography (OCT). In particular, our numerical experiments illustrate the importance of penalisation for OCT reconstruction.

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Section: Performance Resultsmentioning

confidence: 76%

Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

2020

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“…The proposed method in this work was developed based on the configurations of two varying hyperparameters, in order to reduce the level of complexity for an initial proof of concept. Compared to our previous studies for parameter selection in [ 11 ], the proposed method in this work offers lower computational time while providing the same optimal parameters.…”

Section: Discussionmentioning

confidence: 93%

“…The TV algorithm used is the AwPCSD algorithm that was developed earlier [ 7 , 8 , 11 ]. This algorithm is available in an open access software TIGRE toolbox: a MATLAB/Python GPU toolbox for X-ray CT image reconstruction [ 20 ].…”

Section: Background and Related Workmentioning

confidence: 99%

“…The AwPCSD algorithm [ 7 , 11 ] requires the following five hyperparameters to implement the algorithm:…”

Section: Background and Related Workmentioning

confidence: 99%

“…In addition, most of the hyperparameters are data-specific which makes it almost impossible to apply the same set of hyperparameters to data with different scanning scenarios, let alone different anatomical sites. Manual adjusting of the hyperparameters for iterative algorithms is commonly found in many studies [ 9 , 10 ]; a Freund and Shapire’s hedge approach was shown in [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

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Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography

Lohvithee

Sun

Chretien

et al. 2021

Sensors

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In this paper, a computer-aided training method for hyperparameter selection of limited data X-ray computed tomography (XCT) reconstruction was proposed. The proposed method employed the ant colony optimisation (ACO) approach to assist in hyperparameter selection for the adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm, which is a total-variation (TV) based regularisation algorithm. During the implementation, there was a colony of artificial ants that swarm through the AwPCSD algorithm. Each ant chose a set of hyperparameters required for its iterative CT reconstruction and the correlation coefficient (CC) score was given for reconstructed images compared to the reference image. A colony of ants in one generation left a pheromone through its chosen path representing a choice of hyperparameters. Higher score means stronger pheromones/probabilities to attract more ants in the next generations. At the end of the implementation, the hyperparameter configuration with the highest score was chosen as an optimal set of hyperparameters. In the experimental results section, the reconstruction using hyperparameters from the proposed method was compared with results from three other cases: the conjugate gradient least square (CGLS), the AwPCSD algorithm using the set of arbitrary hyperparameters and the cross-validation method.The experiments showed that the results from the proposed method were superior to those of the CGLS algorithm and the AwPCSD algorithm using the set of arbitrary hyperparameters. Although the results of the ACO algorithm were slightly inferior to those of the cross-validation method as measured by the quantitative metrics, the ACO algorithm was over 10 times faster than cross—Validation. The optimal set of hyperparameters from the proposed method was also robust against an increase of noise in the data and can be applicable to different imaging samples with similar context. The ACO approach in the proposed method was able to identify optimal values of hyperparameters for a dataset and, as a result, produced a good quality reconstructed image from limited number of projection data. The proposed method in this work successfully solves a problem of hyperparameters selection, which is a major challenge in an implementation of TV based reconstruction algorithms.

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Low tubal rank tensor recovery using the Bürer-Monteiro factorisation approach. Application to optical coherence tomography

Assoweh

Chrétien

Tamadazte

2022

Journal of Computational and Applied Mathematics

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Efficient Hyper-Parameter Selection in Total Variation-Penalised XCT Reconstruction Using Freund and Shapire’s Hedge Approach

Cited by 5 publications

References 36 publications

Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography

Low tubal rank tensor recovery using the Bürer-Monteiro factorisation approach. Application to optical coherence tomography

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