Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography
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 multi-linear image model rather than a more standard "stacked vector" representation in order to develop novel tensor-based regularizers. Specifically, we model the multi-spectral unknown as a 3-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 two dimensional counterpart, is a convex function of the multi-spectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers (ADMM) approach. Simulation results shows that the generalized tensor nuclear norm can be used as a stand alone regularization technique for the energy selective (spectral) computed tomography (CT) 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.
Code (0)
등록된 구현이 없습니다.
Tasks
Computed Tomography (CT)Similar Papers 제목 키워드 기반
Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations
Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the d…
Computational EfficiencyMRI ReconstructionLow-Rank Tensor Completion by Truncated Nuclear Norm Regularization
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous…
Truncated nuclear norm regularization for low-rank tensor completion
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward sever…
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the …
Tensor Q-Rank: New Data Dependent Definition of Tensor Rank
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the t…