When the number of projections does not satisfy the Shannon/Nyquist sampling requirement, streaking artifacts are inevitable in x-ray computed tomography (CT) images reconstructed using filtered ...backprojection algorithms. In this letter, the spatial-temporal correlations in dynamic CT imaging have been exploited to sparsify dynamic CT image sequences and the newly proposed compressed sensing (CS) reconstruction method is applied to reconstruct the target image sequences. A prior image reconstructed from the union of interleaved dynamical data sets is utilized to constrain the CS image reconstruction for the individual time frames. This method is referred to as prior image constrained compressed sensing (PICCS). In vivo experimental animal studies were conducted to validate the PICCS algorithm, and the results indicate that PICCS enables accurate reconstruction of dynamic CT images using about 20 view angles, which corresponds to an undersampling factor of 32. This undersampling factor implies a potential radiation dose reduction by a factor of 32 in myocardial CT perfusion imaging.
Background
Accurate noise power spectra (NPS) measurement in clinical X‐ray CT exams is challenging due to the need for repeated scans, which expose patients to high radiation risks. A reliable ...method for single CT acquisition NPS estimation is thus highly desirable.
Purpose
To develop a method for estimating local NPS from a single photon counting detector‐CT (PCD‐CT) acquisition.
Methods
A novel nearly statistical bias‐free estimator was constructed from the raw counts data of PCD‐CT scan to estimate the variance of sinogram projection data. An analytical algorithm is employed to reconstruct point‐wise covariance cov(xi,xj)$\text{cov}({\bf x}_i,{\bf x}_j)$ between any two image pixel/voxel locations xi${\bf x}_i$ and xj${\bf x_j}$. A Fourier transform is applied to obtain the desired point‐wise NPS for any chosen location xi${\bf x}_i$. The method was validated using experimental data acquired from a benchtop PCD‐CT system with various physical phantoms, and the results were compared with the conventional local NPS measurement method using repeated scans and statistical ensemble averaging.
Results
The experimental results demonstrate that (1) the proposed method can achieve pointwise/local NPS measurement for a region of interest (ROI) located at any chosen position, accurately characterizing the NPS with spatial structures resulting from image content heterogeneity; (2) the local NPS measured using the proposed method show a higher precision in the measured NPS compared to the conventional measurement method; (3) spatial averaging of the local NPS yields the conventional NPS for a given local ROI.
Conclusion
A new method was developed to enable local NPS from a single PCD‐CT acquisition.
Background
Conventional methods for estimating the noise power spectrum (NPS) often necessitate multiple computed tomography (CT) data acquisitions and are required to satisfy stringent stationarity ...and ergodicity conditions, which prove challenging in CT imaging systems.
Purpose
The aim was to revisit the conventional NPS estimation method, leading to a new framework that estimates local NPS without relying on stationarity or ergodicity, thus facilitating experimental NPS estimations.
Methods
The scientific foundation of the conventional CT NPS measurement method, based on the Wiener‐Khintchine theorem, was reexamined, emphasizing the critical conditions of stationarity and ergodicity. This work proposes an alternative framework, characterized by its independence from stationarity and ergodicity, and its ability to facilitate local NPS estimations. A spatial average of local NPS over a Region of Interest (ROI) yields the conventional NPS for that ROI. The connections and differences between the proposed alternative method and the conventional method are discussed. Experimental studies were conducted to validate the new method.
Results
(1) The NPS estimated using the conventional method was demonstrated to correspond to the spatial average of pointwise NPS from the proposed NPS estimation framework. (2) The NPS estimated over an ROI with the conventional method was shown to be the sum of the NPS estimated from the proposed method and a contribution from measurement uncertainty. (3) Local NPS estimations from the proposed method in this work elucidate the impact of surrounding image content on local NPS variations.
Conclusion
The NPS estimation method proposed in this work allows for the estimation of local NPS without relying on stationarity and ergodicity conditions, offering local NPS estimations with significantly improved precision.
Purpose:
To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its ...nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system.
Methods:
Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo®, GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods.
Results:
(1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a “redder” NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose)−β with the component β ≈ 0.25, which violated the classical σ ∝ (dose)−0.5 power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2.
Conclusions:
The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.
Background: Sparse‐view CT image reconstruction problems encountered in dynamic CT acquisitions are technically challenging. Recently, many deep learning strategies have been proposed to reconstruct ...CT images from sparse‐view angle acquisitions showing promising results. However, two fundamental problems with these deep learning reconstruction methods remain to be addressed: (1) limited reconstruction accuracy for individual patients and (2) limited generalizability for patient statistical cohorts.
Purpose: The purpose of this work is to address the previously mentioned challenges in current deep learning methods.
Methods: A method that combines a deep learning strategy with prior image constrained compressed sensing (PICCS) was developed to address these two problems. In this method, the sparse‐view CT data were reconstructed by the conventional filtered backprojection (FBP) method first, and then processed by the trained deep neural network to eliminate streaking artifacts. The outputs of the deep learning architecture were then used as the needed prior image in PICCS to reconstruct the image. If the noise level from the PICCS reconstruction is not satisfactory, another light duty deep neural network can then be used to reduce noise level. Both extensive numerical simulation data and human subject data have been used to quantitatively and qualitatively assess the performance of the proposed DL‐PICCS method in terms of reconstruction accuracy and generalizability.
Results: Extensive evaluation studies have demonstrated that: (1) quantitative reconstruction accuracy of DL‐PICCS for individual patient is improved when it is compared with the deep learning methods and CS‐based methods; (2) the false‐positive lesion‐like structures and false negative missing anatomical structures in the deep learning approaches can be effectively eliminated in the DL‐PICCS reconstructed images; and (3) DL‐PICCS enables a deep learning scheme to relax its working conditions to enhance its generalizability.
Conclusions: DL‐PICCS offers a promising opportunity to achieve personalized reconstruction with improved reconstruction accuracy and enhanced generalizability.
Background
In recent years, deep learning strategies have been combined with either the filtered backprojection or iterative methods or the direct projection‐to‐image by deep learning only to ...reconstruct images. Some of these methods can be applied to address the interior reconstruction problems for centered regions of interest (ROIs) with fixed sizes. Developing a method to enable interior tomography with arbitrarily located ROIs with nearly arbitrary ROI sizes inside a scanning field of view (FOV) remains an open question.
Purpose
To develop a new pathway to enable interior tomographic reconstruction for arbitrarily located ROIs with arbitrary sizes using a single trained deep neural network model.
Methods
The method consists of two steps. First, an analytical weighted backprojection reconstruction algorithm was developed to perform domain transform from divergent fan‐beam projection data to an intermediate image feature space, B(x⃗)$B(\vec{x})$, for an arbitrary size ROI at an arbitrary location inside the FOV. Second, a supervised learning technique was developed to train a deep neural network architecture to perform deconvolution to obtain the true image f(x⃗)$f(\vec{x})$ from the new feature space B(x⃗)$B(\vec{x})$. This two‐step method is referred to as Deep‐Interior for convenience. Both numerical simulations and experimental studies were performed to validate the proposed Deep‐Interior method.
Results
The results showed that ROIs as small as a diameter of 5 cm could be accurately reconstructed (similarity index 0.985 ± 0.018 on internal testing data and 0.940 ± 0.025 on external testing data) at arbitrary locations within an imaging object covering a wide variety of anatomical structures of different body parts. Besides, ROIs of arbitrary size can be reconstructed by stitching small ROIs without additional training.
Conclusion
The developed Deep‐Interior framework can enable interior tomographic reconstruction from divergent fan‐beam projections for short‐scan and super‐short‐scan acquisitions for small ROIs (with a diameter larger than 5 cm) at an arbitrary location inside the scanning FOV with high quantitative reconstruction accuracy.
Due to the nonlinear nature of the logarithmic operation and the stochastic nature of photon counts (N), sinogram data of photon counting detector CT (PCD-CT) are intrinsically biased, which leads to ...statistical CT number biases. When raw counts are available, nearly unbiased statistical estimators for projection data were developed recently to address the CT number bias issue. However, for most clinical PCD-CT systems, users' access to raw detector counts is limited. Therefore, it remains a challenge for end users to address the CT number bias issue in clinical applications.
To develop methods to correct statistical biases in PCD-CT without requiring access to raw PCD counts.
(1) The sample variance of air-only post-log sinograms was used to estimate air-only detector counts,
. (2) If the post-log sinogram data, y, is available, then N of each detector pixel was estimated using
. Once N was estimated, a closed-form analytical bias correction was applied to the sinogram. (3) If a patient's post-log sinogram data are not archived, a forward projection of the bias-contaminated CT image was used to perform a first-order bias correction. Both the proposed sinogram domain- and image domain-based bias correction methods were validated using experimental PCD-CT data.
Experimental results demonstrated that both sinogram domain- and image domain-based bias correction methods enabled reduced-dose PCD-CT images to match the CT numbers of reference-standard images within -5, 5 HU. In contrast, uncorrected reduced-dose PCD-CT images demonstrated biases ranging from -25 to 55 HU, depending on the material. No increase in image noise or spatial resolution degradation was observed using the proposed methods.
CT number bias issues can be effectively addressed using the proposed sinogram or image domain method in PCD-CT, allowing PCD-CT acquired at different radiation dose levels to have consistent CT numbers desired for quantitative imaging.
Purpose:
Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this ...paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks.
Methods:
The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64‐slice clinical CT scanner at four different dose levels CTDIvol =4, 8, 12, 16 (mGy). Both filtered backprojection (FBP) and MBIR (Veo®, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade‐off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain‐based channelized Hotelling observer (CHO) detectability index d′.
Results:
(1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade‐off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels.
Conclusions:
Due to the intrinsic nonlinearity of the MBIR method, many well‐known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise‐resolution trade‐off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.
When more than two elemental materials are present in a given object, material quantification may not be robust and accurate when the routine two-material decomposition scheme in current dual energy ...CT imaging is employed. In this work, we present an innovative scheme to accomplish accurate three-material decomposition with measurements from a dual energy differential phase contrast CT (DE-DPC-CT) acquisition. A DE-DPC-CT system was constructed using a grating interferometer and a photon counting CT imaging system with two energy bins. The DE-DPC-CT system can simultaneously measure both the imaginary and the real part of the complex refractive index to enable a three-material decomposition. Physical phantom with 21 material inserts were constructed and measured using DE-DPC-CT system. Results demonstrated excellent accuracy in elemental material quantification. For example, relative root-mean-square errors of 4.5% for calcium and 5.2% for iodine were achieved using the proposed three-material decomposition scheme. Biological tissues with iodine inserts were used to demonstrate the potential utility of the proposed spectral CT imaging method. Experimental results showed that the proposed method correctly differentiates the bony structure, iodine, and the soft tissue in the biological specimen samples. A triple spectra CT scan was also performed to benchmark the performance of the DE-DPC-CT scan. Results demonstrated that the material decomposition from the DE-DPC-CT has a much lower quantification noise than that from the triple spectra CT scan.
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