51 research outputs found
Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction
Spectral computed tomography (CT) reconstructs material-dependent attenuation
images with the projections of multiple narrow energy windows, it is meaningful
for material identification and decomposition. Unfortunately, the multi-energy
projection dataset always contains strong complicated noise and result in the
projections has a lower signal-noise-ratio (SNR). Very recently, the
spatial-spectral cube matching frame (SSCMF) was proposed to explore the
non-local spatial-spectrum similarities for spectral CT. The method constructs
such a group by clustering up a series of non-local spatial-spectrum cubes. The
small size of spatial patch for such a group make SSCMF fails to encode the
sparsity and low-rank properties. In addition, the hard-thresholding and
collaboration filtering operation in the SSCMF are also rough to recover the
image features and spatial edges. While for all steps are operated on 4-D
group, we may not afford such huge computational and memory load in practical.
To avoid the above limitation and further improve image quality, we first
formulate a non-local cube-based tensor instead of the group to encode the
sparsity and low-rank properties. Then, as a new regularizer,
Kronecker-Basis-Representation (KBR) tensor factorization is employed into a
basic spectral CT reconstruction model to enhance the ability of extracting
image features and protecting spatial edges, generating the non-local low-rank
cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman
strategy is adopted to solve the NLCTF model. Both numerical simulations and
realistic preclinical mouse studies are performed to validate and assess the
NLCTF algorithm. The results show that the NLCTF method outperforms the other
competitors
Low-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 studies
have suggested several definitions of tensor nuclear norm. However, they have
limitations and may not properly approximate the real rank of a tensor.
Besides, they do not explicitly use the low-rank property in optimization. It
is proved that the recently proposed truncated nuclear norm (TNN) can replace
the traditional nuclear norm, as a better estimation to the rank of a matrix.
Thus, this paper presents a new method called the tensor truncated nuclear norm
(T-TNN), which proposes a new definition of tensor nuclear norm and extends the
truncated nuclear norm from the matrix case to the tensor case. Beneficial from
the low rankness of TNN, our approach improves the efficacy of tensor
completion. We exploit the previously proposed tensor singular value
decomposition and the alternating direction method of multipliers in
optimization. Extensive experiments on real-world videos and images demonstrate
that the performance of our approach is superior to those of existing methods.Comment: Accepted as a poster presentation at the 24th International
Conference on Pattern Recognition in 20-24 August 2018, Beijing, Chin
A Splitting-Based Iterative Algorithm for GPU-Accelerated Statistical Dual-Energy X-Ray CT Reconstruction
When dealing with material classification in baggage at airports, Dual-Energy
Computed Tomography (DECT) allows characterization of any given material with
coefficients based on two attenuative effects: Compton scattering and
photoelectric absorption. However, straightforward projection-domain
decomposition methods for this characterization often yield poor
reconstructions due to the high dynamic range of material properties
encountered in an actual luggage scan. Hence, for better reconstruction quality
under a timing constraint, we propose a splitting-based, GPU-accelerated,
statistical DECT reconstruction algorithm. Compared to prior art, our main
contribution lies in the significant acceleration made possible by separating
reconstruction and decomposition within an ADMM framework. Experimental
results, on both synthetic and real-world baggage phantoms, demonstrate a
significant reduction in time required for convergence
Deep Learning based Spectral CT Imaging
Spectral computed tomography (CT) has attracted much attention in radiation
dose reduction, metal artifacts removal, tissue quantification and material
discrimination. The x-ray energy spectrum is divided into several bins, each
energy-bin-specific projection has a low signal-noise-ratio (SNR) than the
current-integrating counterpart, which makes image reconstruction a unique
challenge. Traditional wisdom is to use prior knowledge based iterative
methods. However, this kind of methods demands a great computational cost.
Inspired by deep learning, here we first develop a deep learning based
reconstruction method; i.e., U-net with L_p^p-norm, Total variation, Residual
learning, and Anisotropic adaption (ULTRA). Specifically, we emphasize the
Various Multi-scale Feature Fusion and Multichannel Filtering Enhancement with
a denser connection encoding architecture for residual learning and feature
fusion. To address the image deblurring problem associated with the
-loss, we propose a general -loss, Furthermore, the images
from different energy bins share similar structures of the same object, the
regularization characterizing correlations of different energy bins is
incorporated into the -loss function, which helps unify the deep
learning based methods with traditional compressed sensing based methods.
Finally, the anisotropically weighted total variation is employed to
characterize the sparsity in the spatial-spectral domain to regularize the
proposed network. In particular, we validate our ULTRA networks on three
large-scale spectral CT datasets, and obtain excellent results relative to the
competing algorithms. In conclusion, our quantitative and qualitative results
in numerical simulation and preclinical experiments demonstrate that our
proposed approach is accurate, efficient and robust for high-quality spectral
CT image reconstruction
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 several
definitions of tensor nuclear norm. However, they are limited and may not
accurately approximate the real rank of a tensor, and they do not explicitly
use the low-rank property in optimization. It is proved that the recently
proposed truncated nuclear norm (TNN) can replace the traditional nuclear norm,
as an improved approximation to the rank of a matrix. In this paper, we propose
a new method called the tensor truncated nuclear norm (T-TNN), which suggests a
new definition of tensor nuclear norm. The truncated nuclear norm is
generalized from the matrix case to the tensor case. With the help of the low
rankness of TNN, our approach improves the efficacy of tensor completion. We
adopt the definition of the previously proposed tensor singular value
decomposition, the alternating direction method of multipliers, and the
accelerated proximal gradient line search method in our algorithm. Substantial
experiments on real-world videos and images illustrate that the performance of
our approach is better than those of previous methods.Comment: arXiv admin note: substantial text overlap with arXiv:1712.0070
DECT-MULTRA: Dual-Energy CT Image Decomposition With Learned Mixed Material Models and Efficient Clustering
Dual energy computed tomography (DECT) imaging plays an important role in
advanced imaging applications due to its material decomposition capability.
Image-domain decomposition operates directly on CT images using linear matrix
inversion, but the decomposed material images can be severely degraded by noise
and artifacts. This paper proposes a new method dubbed DECT-MULTRA for
image-domain DECT material decomposition that combines conventional penalized
weighted-least squares (PWLS) estimation with regularization based on a mixed
union of learned transforms (MULTRA) model. Our proposed approach pre-learns a
union of common-material sparsifying transforms from patches extracted from all
the basis materials, and a union of cross-material sparsifying transforms from
multi-material patches. The common-material transforms capture the common
properties among different material images, while the cross-material transforms
capture the cross-dependencies. The proposed PWLS formulation is optimized
efficiently by alternating between an image update step and a sparse coding and
clustering step, with both of these steps having closed-form solutions. The
effectiveness of our method is validated with both XCAT phantom and clinical
head data. The results demonstrate that our proposed method provides superior
material image quality and decomposition accuracy compared to other competing
methods
A New Low-Rank Tensor Model for Video Completion
In this paper, we propose a new low-rank tensor model based on the circulant
algebra, namely, twist tensor nuclear norm or t-TNN for short. The twist tensor
denotes a 3-way tensor representation to laterally store 2D data slices in
order. On one hand, t-TNN convexly relaxes the tensor multi-rank of the twist
tensor in the Fourier domain, which allows an efficient computation using FFT.
On the other, t-TNN is equal to the nuclear norm of block circulant
matricization of the twist tensor in the original domain, which extends the
traditional matrix nuclear norm in a block circulant way. We test the t-TNN
model on a video completion application that aims to fill missing values and
the experiment results validate its effectiveness, especially when dealing with
video recorded by a non-stationary panning camera. The block circulant
matricization of the twist tensor can be transformed into a circulant block
representation with nuclear norm invariance. This representation, after
transformation, exploits the horizontal translation relationship between the
frames in a video, and endows the t-TNN model with a more powerful ability to
reconstruct panning videos than the existing state-of-the-art low-rank models.Comment: 8 pages, 11 figures, 1 tabl
On the Fusion of Compton Scatter and Attenuation Data for Limited-view X-ray Tomographic Applications
In this paper we demonstrate the utility of fusing energy-resolved
observations of Compton scattered photons with traditional attenuation data for
the joint recovery of mass density and photoelectric absorption in the context
of limited view tomographic imaging applications. We begin with the development
of a physical and associated numerical model for the Compton scatter process.
Using this model, we propose a variational approach recovering these two
material properties. In addition to the typical data-fidelity terms, the
optimization functional includes regularization for both the mass density and
photoelectric coefficients. We consider a novel edge-preserving method in the
case of mass density. To aid in the recovery of the photoelectric information,
we draw on our recent method in \cite{r15} and employ a non-local
regularization scheme that builds on the fact that mass density is more stably
imaged. Simulation results demonstrate clear advantages associated with the use
of both scattered photon data and energy resolved information in mapping the
two material properties of interest. Specifically, comparing images obtained
using only conventional attenuation data with those where we employ only
Compton scatter photons and images formed from the combination of the two,
shows that taking advantage of both types of data for reconstruction provides
far more accurate results
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
unfoldings of the tensor. We show that this approach can be substantially
suboptimal: reliably recovering a -way tensor of length and Tucker rank
from Gaussian measurements requires observations. In
contrast, a certain (intractable) nonconvex formulation needs only observations. We introduce a very simple, new convex relaxation, which
partially bridges this gap. Our new formulation succeeds with observations. While these results pertain to
Gaussian measurements, simulations strongly suggest that the new norm also
outperforms the sum of nuclear norms for tensor completion from a random subset
of entries.
Our lower bound for the sum-of-nuclear-norms model follows from a new result
on recovering signals with multiple sparse structures (e.g. sparse, low rank),
which perhaps surprisingly demonstrates the significant suboptimality of the
commonly used recovery approach via minimizing the sum of individual sparsity
inducing norms (e.g. , nuclear norm). Our new formulation for low-rank
tensor recovery however opens the possibility in reducing the sample complexity
by exploiting several structures jointly.Comment: Slight modifications are made in this second version (mainly, Lemma
5
Low-dose spectral CT reconstruction using L0 image gradient and tensor dictionary
Spectral computed tomography (CT) has a great superiority in lesion
detection, tissue characterization and material decomposition. To further
extend its potential clinical applications, in this work, we propose an
improved tensor dictionary learning method for low-dose spectral CT
reconstruction with a constraint of image gradient L0-norm, which is named as
L0TDL. The L0TDL method inherits the advantages of tensor dictionary learning
(TDL) by employing the similarity of spectral CT images. On the other hand, by
introducing the L0-norm constraint in gradient image domain, the proposed
method emphasizes the spatial sparsity to overcome the weakness of TDL on
preserving edge information. The alternative direction minimization method
(ADMM) is employed to solve the proposed method. Both numerical simulations and
real mouse studies are perform to evaluate the proposed method. The results
show that the proposed L0TDL method outperforms other competing methods, such
as total variation (TV) minimization, TV with low rank (TV+LR), and TDL
methods
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