Yanbo Zhang

Tensor-Based Dictionary Learning for Spectral CT Reconstruction

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.

Tensor-based dictionary learning for dynamic tomographic reconstruction

In dynamic computed tomography (CT) reconstruction, the data acquisition speed limits the spatio-temporal resolution. Recently, compressed sensing theory has been instrumental in improving CT reconstruction from far few-view projections. In this paper, we present an adaptive method to train a tensor-based spatio-temporal dictionary for sparse representation of an image sequence during the reconstruction process. The correlations among atoms and across phases are considered to capture the characteristics of an object. The reconstruction problem is solved by the alternating direction method of multipliers. To recover fine or sharp structures such as edges, the nonlocal total variation is incorporated into the algorithmic framework. Preclinical examples including a sheep lung perfusion study and a dynamic mouse cardiac imaging demonstrate that the proposed approach outperforms the vectorized dictionary-based CT reconstruction in the case of few-view reconstruction.

Data consistency condition–based beam-hardening correction

In medical x ray computed tomography (CT) imaging devices, the x ray tube usually emits a polychromatic spectrum of photons result- ing in beam-hardening artifacts in the reconstructed images. The bone- correction method has been widely adopted to compensate for beam- hardening artifacts. However, its correction performance is highly depen- dent on the empirical determination of a scaling factor, which is used to adjust the ratio of the reconstructed value in the bone region to the actual mass density of bone-tissue. A significant problem with bone-correction is that a large number of physical experiments are routinely required to accurately calibrate the scaling factor. In this article, an improved bone- correction method is proposed, based on the projection data consistency condition, to automatically determine the scaling factor. Extensive numer- ical simulations have verified the existence of an optimal scaling factor, the sensitivity of bone-correction to the scaling factor, and the efficiency of the proposed method for the beam-hardening correction. C 2011 Society

An adaptive reconstruction algorithm for spectral CT regularized by a reference image

The photon counting detector based spectral CT system is attracting increasing attention in the CT field. However, the spectral CT is still premature in terms of both hardware and software. To reconstruct high quality spectral images from low-dose projections, an adaptive image reconstruction algorithm is proposed that assumes a known reference image (RI). The idea is motivated by the fact that the reconstructed images from different spectral channels are highly correlated. If a high quality image of the same object is known, it can be used to improve the low-dose reconstruction of each individual channel. This is implemented by maximizing the patch-wise correlation between the object image and the RI. Extensive numerical simulations and preclinical mouse study demonstrate the feasibility and merits of the proposed algorithm. It also performs well for truncated local projections, and the surrounding area of the region- of-interest (ROI) can be more accurately reconstructed. Furthermore, a method is introduced to adaptively choose the step length, making the algorithm more feasible and easier for applications.

Weighted Total Variation constrained reconstruction for reduction of metal artifact in CT

TV constrained reconstruction could obtain perfect results from incomplete data, and has been applied to reduce metal artifact by assuming that the projection contaminated by metal is missing. In TV constrained reconstruction, the selection of a proper step parameter for TV minimization procedure is a key point. However, this parameter is usually selected empirically, and it is a constant for all pixels in the whole image domain, regardless of the difference of missing projection quantity at different pixels. By analyzing the relationship between the missing projections and pixels position, a Weighted Total Variation (WTV) constrained reconstruction method is proposed to reduce metal artifact in this paper. For WTV constrained method, the parameters are no longer the same, but vary over image domain as the introduced information miss rate. The simulation results show that the proposed method is more effective than current TV constraint to reduce metal artifact. Moreover, WTV constrained method is extended to other incomplete projection problems.

Beam hardening correction for fan-beam CT imaging with multiple materials

In X-ray CT, Beam hardening (BH) effect, which is caused by polychromatic X-ray beam and energy-dependent attenuation coefficients, always introduces cupping and streak artifacts. Most of correction methods can only deal with beam hardening artifacts for a single material or dual-material object, but fail to correct in case of a multi-material object since the correction complexity and instability increase with the increase of the kinds of materials. In this paper, we proposed a multimaterial BH correction method. A binary Legendre polynomial is adopted to correct BH based on bi-parameter imaging physical model, and the Helgasson-Ludwig consistency condition (H-L consistency condition) is introduced to optimally determine the bi-parameters of all materials. In the simulation experiments showed that the proposed method can suppress the artifacts greatly. The corrected values approach very closely to the ideal ones.

Low-dose CT reconstruction based on multiscale dictionary

Statistical CT reconstruction using penalized weighted least-squares(PWLS) criteria can improve image-quality in low-dose CT reconstruction. A suitable design of regularization term can benefit it very much. Recently, sparse representation based on dictionary learning has been treated as the regularization term and results in a high quality reconstruction. In this paper, we incorporated a multiscale dictionary into statistical CT reconstruction, which can keep more details compared with the reconstruction based on singlescale dictionary. Further more, we exploited reweigted l1 norm minimization for sparse coding, which performs better than I norm minimization in locating the sparse solution of underdetermined linear systems of equations. To mitigate the time consuming process that computing the gradiant of regularization term, we adopted the so-called double surrogates method to accelerate ordered-subsets image reconstruction. Experiments showed that combining multiscale dictionary and reweighted l1 norm minimization can result in a reconstruction superior to that bases on singlescale dictionary and l1 norm minimization.

Metal artifact reduction based on beam hardening correction and statistical iterative reconstruction for X-ray computed tomography

Metal artifact is a main cause to degrade CT image quality, but there is still no standard solution to this issue. The cause of introduction of metal artifacts is due to several physical effects, in which beam hardening and noise are two major factors. Accordingly, in this paper these two factors are alleviated by using beam hardening correction based on polynomial fitting and statistical iterative reconstruction based on Poisson log-likelihood approach. Unlike other metal artifact reduction (MAR) methods by using iterative image reconstruction from polychromatic projection dataset, the proposed method in this work does not require a priori knowledge about the X- ray spectrum and attenuations of the materials to be reconstructed. A conventional linear interpolation MAR algorithm and two MAR methods based on beam hardening correction are performed for comparison. Simulation results illustrate that the proposed method can suppress metal artifacts greatly and restore low contrast tissues well.

A spectral CT denoising algorithm based on weighted block matching 3D filtering

In spectral CT, an energy-resolving detector is capable of counting the number of received photons in different energy channels with appropriate post-processing steps. Because the received photon number in each energy channel is low in practice, the generated projections suffer from low signal-to-noise ratio. This poses a challenge to perform image reconstruction of spectral CT. Because the reconstructed multi-channel images are for the same object but in different energies, there is a high correlation among these images and one can make full use of this redundant information. In this work, we propose a weighted block-matching and three-dimensional (3-D) filtering (BM3D) based method for spectral CT denoising. It is based on denoising of small 3-D data arrays formed by grouping similar 2-D blocks from the whole 3-D data image. This method consists of the following two steps. First, a 2-D image is obtained using the filtered back-projection (FBP) in each energy channel. Second, the proposed weighted BM3D filtering is performed. It not only uses the spatial correlation within each channel image but also exploits the spectral correlation among the channel images. The proposed method is evaluated on both numerical simulation and realistic preclinical datasets, and its merits are demonstrated by the promising results.

Tensor decomposition and nonlocal means based spectral CT reconstruction

As one of the state-of-the-art detectors, photon counting detector is used in spectral CT to classify the received photons into several energy channels and generate multichannel projection simultaneously. However, the projection always contains severe noise due to the low counts in each energy channel. How to reconstruct high-quality images from photon counting detector based spectral CT is a challenging problem. It is widely accepted that there exists self-similarity over the spatial domain in a CT image. Moreover, because a multichannel CT image is obtained from the same object at different energy, images among channels are highly correlated. Motivated by these two characteristics of the spectral CT, we employ tensor decomposition and nonlocal means methods for spectral CT iterative reconstruction. Our method includes three basic steps. First, each channel image is updated by using the OS-SART. Second, small 3D volumetric patches (tensor) are extracted from the multichannel image, and higher-order singular value decomposition (HOSVD) is performed on each tensor, which can help to enhance the spatial sparsity and spectral correlation. Third, in order to employ the self-similarity in CT images, similar patches are grouped to reduce noise using the nonlocal means method. These three steps are repeated alternatively till the stopping criteria are met. The effectiveness of the developed algorithm is validated on both numerically simulated and realistic preclinical datasets. Our results show that the proposed method achieves promising performance in terms of noise reduction and fine structures preservation.