Noise power spectrum (NPS) in computed tomography: Enabling local NPS measurement without stationarity and ergodicity assumptions

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.

Experimental measurement of local noise power spectrum (NPS) in photon counting detector-CT (PCD-CT) using a single data acquisition

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 covariancecov ( x i , x j ) $\text{cov}({\bf x}_i,{\bf x}_j)$ between any two image pixel/voxel locationsx i ${\bf x}_i$ andx j ${\bf x_j}$ . A Fourier transform is applied to obtain the desired point-wise NPS for any chosen locationx i ${\bf x}_i$ . 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.

Method to estimate fan-beam CT noise power spectrum using two basis functions with a limited number of noise realizations

PURPOSE

The noise power spectrum (NPS) plays a key role in image quality (IQ) evaluation as it can be used for predicting detection performance or calculating detective quantum efficiency (DQE). Traditionally, the NPS is estimated by ensemble averaging multiple realizations of noise-only images. However, the estimation error increases when there are a limited number of images. Since the estimation error directly affects the IQ index, an accurate NPS estimation method is required. Recent works have proposed NPS estimation methods using the radial 1D NPS as the basis; however, when sharp kernels are used during image reconstruction, these methods cannot accurately estimate the amplitude of each angular spoke of the 2D NPS composed of different cutoff frequencies determined from the complementary projection magnification factors for different spatial regions. In this work, we propose a 2D NPS estimation method that reflects the accurate amplitude of each angular spoke for fan-beam CT images.

METHODS

An angular spoke of the 2D NPS is composed of two basis functions with different cutoff frequencies determined from the complementary projection magnification factors. The proposed method estimates these two weighting factors for each basis function by minimizing the mean-squared error (MSE) between the 2D NPS estimated from 10 noise realizations. Two noise profiles and two types of apodization filters (i.e., rectangular and Hanning) were used to reconstruct the noise-only images. To examine the nonstationary noise property of fan-beam CT images, the 2D NPS was estimated at three different local regions. The estimation accuracy of the proposed method was further improved by estimating the approximate weighting factors with sinusoidal functions, considering that the weighting factors vary slowly throughout the view angles. Regression orders of 1 to 4 were used during these estimations. The approximate weighting factors were then multiplied with each of the basis functions to estimate the 2D NPS. The normalized mean-squared error (NMSE) was used as an index to compare the performance of each NPS estimation method, with the analytical 2D NPS as the reference. Further validation was performed using XCAT phantom data.

RESULTS

We observed that the 2D NPS estimated using two basis functions reflected the accurate amplitude of each angular spoke, whereas the 2D NPS estimated using the radial 1D NPS as the basis could not. The 2D NPS estimated by applying the approximate weighting factors showed improved performance compared with that estimated using two basis functions. In addition, unlike the view-independent noise cases, where a lower regression order showed higher estimation performance, a higher regression order showed higher estimation performance in the view-dependent noise cases.

CONCLUSIONS

In this work, we propose a 2D NPS estimation method that reflects the accurate amplitude of each angular spoke for fan-beam CT images using two basis functions. We observed that the proposed 2D NPS estimation method using two basis functions achieved better estimation performance compared with the method using the radial 1D NPS as the basis. This article is protected by copyright. All rights reserved.

Ultra-low-dose lung multidetector computed tomography in children - Approaching 0.2 millisievert

PURPOSE

To compare objective and subjective parameters in image quality and radiation dose of two MDCTs (helical 64 detector CT vs. axial 256 detector CT) in paediatric lung CT.

METHODS

Radiation dose and image quality were compared between non-enhanced lung CT from a helical 64-slice multidetector CT (MDCT 1) and a 256-slice scanner (MDCT 2) with axial wide-cone acquisition and using deep learning image reconstruction. In 23 size-matched paediatric studies (age 2-18 years) from each scanner, the radiation exposure, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), image sharpness and delineation of small airways were assessed. Subjective image quality was rated by 6 paediatric radiologists.

RESULTS

While MDCT 2 provided higher SNR and CNR, subjective image quality was not significantly different between studies from both scanners. Radiation exposure was lower in studies from MDCT 2 (CTDIvol 0.26 ± 0.14 mGy, effective dose 0.23 ± 0.11 mSv) than from MDCT 1 (CTDIvol 0.96 ± 0.52 mGy, effective dose 1.13 ± 0.58 mSv), p < 0.001. Despite lower radiation dose for the scout images, the relative scout-scan-ratio increased from 2.64 ± 1.42 % in MDCT 1 to 6.60 ± 5.03 % in MDCT 2 (p = 0.001).

CONCLUSIONS

By using latest scanner technology effective radiation dose can be reduced to 0.1-0.3 mSv for lung CT in children without compromising image quality. Scout image dose increasingly accounts for substantial portions of the total scan dose and needs to be optimized. In children CT should be performed on state-of-the-art MDCT scanners with size-adapted exposure protocols and iterative reconstruction.

Accurate Image Domain Noise Insertion in CT Images

Tools to simulate lower dose, noisy computed tomography (CT) images from existing data enable protocol optimization by quantifying the trade-off between patient dose and image quality. Many studies have developed and validated noise insertion techniques; however, most of these tools operate on proprietary projection data which can be difficult to access and can be time consuming when a large number of realizations is needed. In response, this work aims to develop and validate an image domain approach to accurately insert CT noise and simulate low dose scans. In this framework, information from the image is utilized to estimate the variance map and local noise power spectra (NPS). Normally distributed noise is filtered within small patches in the image domain using the inverse Fourier transform of the square root of the estimated local NPS to generate noise with the appropriate spatial correlation. The patches are overlapped and element-wise multiplied by the standard deviation map to produce locally varying, spatially correlated noise. The resulting noise image is scaled based on the relationship between the initial and desired dose and added to the original image. The results demonstrate excellent agreement between traditional projection domain methods and the proposed method, both for simulated and real data sets. This new framework is not intended to replace projection domain methods; rather, it fills a gap in CT noise simulation tools and is an accurate alternative when projection domain methods are not practical, for example, in large scale repeatability or detectability studies.

A data-efficient method for local noise power spectrum (NPS) estimation in FDK-reconstructed 3D cone-beam CT

PURPOSE

For computed tomography (CT) systems in which noise is nonstationary, a local noise power spectrum (NPS) is often needed to characterize its noise property. We have previously developed a data-efficient radial NPS method to estimate the two-dimensional (2D) local NPS for filtered back projection (FBP)-reconstructed fan-beam CT utilizing the polar separability of CT NPS. In this work, we extend this method to estimate three-dimensional (3D) local NPS for feldkamp-davis-kress (FDK)-reconstructed cone-beam CT (CBCT) volumes.

METHODS

Starting from the 2D polar separability, we analyze the CBCT geometry and FDK image reconstruction process to derive the 3D expression of the polar separability for CBCT local NPS. With the polar separability, the 3D local NPS of CBCT can be decomposed into a 2D radial NPS shape function and a one-dimensional (1D) angular amplitude function with certain geometrical transforms. The 2D radial NPS shape function is a global function characterizing the noise correlation structure, while the 1D angular amplitude function is a local function reflecting the varying local noise amplitudes. The 3D radial local NPS method is constructed from the polar separability. We evaluate the accuracy of the 3D radial local NPS method using simulated and real CBCT data by comparing the radial local NPS estimates to a reference local NPS in terms of normalized mean squared error (NMSE) and a task-based performance metric (lesion detectability).

RESULTS

In both simulated and physical CBCT examples, a very small NMSE (<5%) was achieved by the radial local NPS method from as few as two scans, while for the traditional local NPS method, about 20 scans were needed to reach this accuracy. The results also showed that the detectability-based system performances computed using the local NPS estimated with the NPS method developed in this work from two scans closely reflected the actual system performance.

CONCLUSIONS

The polar separability greatly reduces the data dimensionality of the 3D CBCT local NPS. The radial local NPS method developed based on this property is shown to be capable of estimating the 3D local NPS from only two CBCT scans with acceptable accuracy. The minimum data requirement indicates the potential utility of local NPS in CBCT applications even for clinical situations.

Inverse filtering approach to measure directional in-plane modulation transfer function using a sphere phantom for a digital tomosynthesis system

We propose a method to measure the directional in-plane modulation transfer function (MTF) of a digital tomosynthesis system using a sphere phantom. To assess the spatial resolution of an in-plane image of the tomosynthesis system, projection data of a sphere phantom were generated within a limited data acquisition range of 40°, and reconstructed by the FDK algorithm. To measure the in-plane MTF, we divided the Fourier transform of the reconstructed sphere phantom by that of the ideal sphere phantom, and then performed plane integral along the fz-direction. When dividing, small values in the denominator can introduce estimation errors, and these errors were reduced by the proposed method. To evaluate the performance of the proposed method, the in-plane MTF estimated by simulation and experimental data was compared to the ideal in-plane MTF generated by computer simulations using a point object. For quantitative evaluation, we measured frequency values at half-maximum and full-maximum of the directional in-plane MTF along the three different directions (i.e., f_0° -, f_30° -, and f_60° -directions) and compared them with those of the ideal in-plane MTF. Although the sphere phantom has been regarded as an inappropriate object due to the anisotropic characteristics of tomosynthesis image, our results show that the proposed method has a reliable estimation performance, demonstrating the sphere phantom is still suitable for measuring the directional in-plane MTF for a digital tomosynthesis system.

Evaluation of automatic image quality assessment in chest CT - A human cadaver study

PURPOSE

The evaluation of clinical image quality (IQ) is important to optimize CT protocols and to keep patient doses as low as reasonably achievable. Considering the significant amount of effort needed for human observer studies, automatic IQ tools are a promising alternative. The purpose of this study was to evaluate automatic IQ assessment in chest CT using Thiel embalmed cadavers.

METHODS

Chest CT's of Thiel embalmed cadavers were acquired at different exposures. Clinical IQ was determined by performing a visual grading analysis. Physical-technical IQ (noise, contrast-to-noise and contrast-detail) was assessed in a Catphan phantom. Soft and sharp reconstructions were made with filtered back projection and two strengths of iterative reconstruction. In addition to the classical IQ metrics, an automatic algorithm was used to calculate image quality scores (IQs). To be able to compare datasets reconstructed with different kernels, the IQs values were normalized.

RESULTS

Good correlations were found between IQs and the measured physical-technical image quality: noise (ρ=-1.00), contrast-to-noise (ρ=1.00) and contrast-detail (ρ=0.96). The correlation coefficients between IQs and the observed clinical image quality of soft and sharp reconstructions were 0.88 and 0.93, respectively.

CONCLUSIONS

The automatic scoring algorithm is a promising tool for the evaluation of thoracic CT scans in daily clinical practice. It allows monitoring of the image quality of a chest protocol over time, without human intervention. Different reconstruction kernels can be compared after normalization of the IQs.

Noise Power Characteristics of a Micro-Computed Tomography System

OBJECTIVE

The aim of this study was to investigate the noise power properties of a micro-computed tomography (micro-CT) system under different operating conditions.

METHODS

A commercial micro-CT was used in the study that used a flat panel detector with a 127-μm-pixel pitch and a micro-focus x-ray tube. Conical tubes of various diameters were used under different acquisition conditions. Multidimensional noise power spectrums were used as a metric to investigate the noise properties of the system. Noise power spectrum was calculated from the difference data generated by subtraction of 2 identical scans. The noise properties with respect to various parameters that include the impact of number of projections, x-ray spectra, milliampere-second, slice location, object diameter, voxel size, geometric magnification (M), back-projection filters, and reconstruction magnification (Mrecon) were studied.

RESULTS

At a same isocentric exposure rate of 270 mR/s, the noise power was much lower for the image reconstructed with 3672 views (122 seconds) as compared with the 511 views (17 seconds), whereas at a fixed isocentric exposure of 4600 mR, the noise power levels were almost similar. Image noise with a 50-kV beam was higher as compared with the 90-kV beam at a same isocentric exposure. Image noise from a 16-mm-diameter conical tube was much lower as compared with the 28- and 56-mm tubes under identical isocentric exposures. The choice of back-projection filter influences noise power spectrum curves in terms of width and amplitudes. Reconstruction magnification applied during the reconstruction process increased the noise power at lower spatial frequencies but reduced the noise power at higher spatial frequencies. It can be established that, for small details corresponding to high spatial frequencies, reconstruction magnification can provide an improved signal-to-noise ratio. At all spatial frequencies, the in-plane images had lower noise power levels as compared with the z-plane images.

CONCLUSIONS

The noise power properties investigated in this study provide important image quality references for refined cone beam system development, optimization, and operations.

Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system

PURPOSE

Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction.

METHODS

A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object.

RESULTS

(1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of its NPS was found to be different from that of a peripheral ROI in the centered object, even when the physical positions of the two ROIs relative to the isocenter were the same. (3) The potential clinical impact of the highly anisotropic NPS, caused by the interplay of the bowtie filter and position of the image object, was highlighted in images of specific bar patterns oriented at different angles. The visual perception of the bar patterns was found to be strongly dependent on their orientation.

CONCLUSIONS

The NPS of CT depends strongly on the bowtie filter and object position. Even if the location of the ROI with respect to the isocenter is fixed, there can be different symmetries in the NPS, which depend on the object position and the size of the bowtie filter. For an isolated off-centered object, the NPS of its CT images cannot be represented by the NPS measured from a centered object.