Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography

By Oguz Semerci, Ning Hao, Misha Elena Kilmer, Eric Lawrence Miller. IEEE Transactions on Image Processing, 2013

392 citations recorded by the source corpus.

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a tensor-based iterative algorithm that simultaneously reconstructs the X-ray attenuation distribution for each energy. We use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor-based regularizers. In particular, we model the multispectral unknown as a three-way tensor where the first two dimensions are space and the third dimension is energy. This approach allows for the design of tensor nuclear norm regularizers, which like its 2D counterpart, is a convex function of the multispectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach. Simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective (spectral) computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent.

Subfields: Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/ba1d3f3ae262029b0ab5b58e3f8066016374de89

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Zhouchen Lin
2. Canyi Lu
3. Shuicheng Yan
4. Jiashi Feng
5. Yudong Chen
6. Shuchin Aeron
7. Wei David Liu
8. Zemin Zhang

In Radiology, Nuclear Medicine and Imaging

1. Yimin Wei
2. John Wright
3. Shuicheng Yan
4. Yun Miao
5. Pan Zhou
6. Chao Zhang
7. Jiashi Feng
8. Canyi Lu

Citations in the corpus

• T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product (2019, methodology): “Semerci, Hao, Kilmer and Miller [34] introduced the tensor-based formulation and used the ADMM algorithm to solve the TNN model.”
• Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm (2018, result): “The above TNN definition is also different from existing works [19], [34], [27].”
• Generalized tensor function via the tensor singular value decomposition based on the T-product (2019, methodology): “Semerci, Hao, Kilmer and Miller [46] introduced the tensor-based formulation and used the ADMM algorithm to solve the TNN model.”
• Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (2016, methodology): “With the factor 1/n3, our tensor nuclear norm definition is different from previous work [24, 28].”
• Tensor Factorization for Low-Rank Tensor Completion (2018, background): “[34] developed a new tensor nuclear norm (TNN).”
• Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery (2013, methodology): “, 2011) and applied to various datasets in imaging (Semerci et al., 2013; Kreimer & Sacchi, 2013; Li & Li, 2010; Li et al., 2010).”
• Exact Tensor Completion Using t-SVD (2015, background): “15 (Tubal nuclear norm [30]): The tubal nuclear norm of a tensor A, denoted as ‖A‖T NN , is the sum of singular values of all the frontal slices of Â, and is a convex relaxation of the tensor tubal-rank [8].”