PurposeRecent research explores using neural networks to reconstruct undersampled magnetic resonance imaging. Because of the complexity of the artifacts in the reconstructed images, there is a need to develop task-based approaches to image quality. We compared conventional global quantitative metrics to evaluate image quality in undersampled images generated by a neural network with human observer performance in a detection task. The purpose is to study which acceleration (2×, 3×, 4×, 5×) would be chosen with the conventional metrics and compare it to the acceleration chosen by human observer performance.ApproachWe used common global metrics for evaluating image quality: the normalized root mean squared error (NRMSE) and structural similarity (SSIM). These metrics are compared with a measure of image quality that incorporates a subtle signal for a specific task to allow for image quality assessment that locally evaluates the effect of undersampling on a signal. We used a U-Net to reconstruct under-sampled images with 2×, 3×, 4×, and 5× one-dimensional undersampling rates. Cross-validation was performed for a 500- and a 4000-image training set with both SSIM and MSE losses. A two-alternative forced choice (2-AFC) observer study was carried out for detecting a subtle signal (small blurred disk) from images with the 4000-image training set.ResultsWe found that for both loss functions, the human observer performance on the 2-AFC studies led to a choice of a 2× undersampling, but the SSIM and NRMSE led to a choice of a 3× undersampling.ConclusionsFor this detection task using a subtle small signal at the edge of detectability, SSIM and NRMSE led to an overestimate of the achievable undersampling using a U-Net before a steep loss of image quality between 2×, 3×, 4×, 5× undersampling rates when compared to the performance of human observers in the detection task.
KEYWORDS: Performance modeling, Magnetic resonance imaging, Data acquisition, Aliasing, Modeling, Image restoration, Signal detection, Education and training, Statistical modeling
Undersampling in the frequency domain (k-space) in MRI enables faster data acquisition. In this study, we used a fixed 1D undersampling factor of 5x with only 20% of the k-space collected. The fraction of fully acquired low k-space frequencies were varied from 0% (all aliasing) to 20% (all blurring). The images were reconstructed using a multi-coil SENSE algorithm. We used two-alternative forced choice (2-AFC) and the forced localization tasks with a subtle signal to estimate the human observer performance. The 2-AFC average human observer performance remained fairly constant across all imaging conditions. The forced localization task performance improved from the 0% condition to the 2.5% condition and remained fairly constant for the remaining conditions, suggesting that there was a decrease in task performance only in the pure aliasing situation. We modeled the average human performance using a sparse-difference of Gaussians (SDOG) Hotelling observer model. Because the blurring in the undersampling direction makes the mean signal asymmetric, we explored an adaptation for irregular signals that made the SDOG template asymmetric. To improve the observer performance, we also varied the number of SDOG channels from 3 to 4. We found that despite the asymmetry in the mean signal, both the symmetric and asymmetric models reasonably predicted the human performance in the 2-AFC experiments. However, the symmetric model performed slightly better. We also found that a symmetric SDOG model with 4 channels implemented using a spatial domain convolution and constrained to the possible signal locations reasonably modeled the forced localization human observer results.
Undersampling in the frequency domain (k-space) in MRI accelerates the data acquisition. Typically, a fraction of the low frequencies is fully collected and the rest are equally undersampled. We used a fixed 1D undersampling factor of 5x where 20% of the k-space lines are collected but varied the fraction of the low k-space frequencies that are fully sampled. We used a range of fully acquired low k-space frequencies from 0% where the primary artifact is aliasing to 20% where the primary artifact is blurring in the undersampling direction. Small lesions were placed in the coil k-space data for fluid-attenuated inversion recovery (FLAIR) brain images from the fastMRI database. The images were reconstructed using a multi-coil SENSE reconstruction with no regularization. We conducted a human observer two-alternative forced choice (2-AFC) study with a signal known exactly and a search task with variable backgrounds for each of the acquisitions. We found that for the 2-AFC task, the average human observer did better with more of the low frequencies being fully sampled. For the search task, we found that after an initial improvement from having none of the low frequencies fully sampled to just 2.5%, the performance remained fairly constant. We found that the performance in the two tasks had a different relationship to the acquired data. We also found that the search task was more consistent with common practice in MRI where a range of frequencies between 5% and 10% of the low frequencies are fully sampled.
KEYWORDS: Wavelets, Image restoration, Magnetic resonance imaging, Image quality, Signal detection, Modeling, Performance modeling, Data modeling, Signal to noise ratio, Medical image reconstruction
PurposeTask-based assessment of image quality in undersampled magnetic resonance imaging provides a way of evaluating the impact of regularization on task performance. In this work, we evaluated the effect of total variation (TV) and wavelet regularization on human detection of signals with a varying background and validated a model observer in predicting human performance.ApproachHuman observer studies used two-alternative forced choice (2-AFC) trials with a small signal known exactly task but with varying backgrounds for fluid-attenuated inversion recovery images reconstructed from undersampled multi-coil data. We used a 3.48 undersampling factor with TV and a wavelet sparsity constraints. The sparse difference-of-Gaussians (S-DOG) observer with internal noise was used to model human observer detection. The internal noise for the S-DOG was chosen to match the average percent correct (PC) in 2-AFC studies for four observers using no regularization. That S-DOG model was used to predict the PC of human observers for a range of regularization parameters.ResultsWe observed a trend that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. A similar result was found for the normalized ensemble root mean squared error. Without changing the internal noise, the model observer tracked the performance of the human observers as the regularization was increased but overestimated the PC for large amounts of regularization for TV and wavelet sparsity, as well as the combination of both parameters.ConclusionsFor the task we studied, the S-DOG observer was able to reasonably predict human performance with both TV and wavelet sparsity regularizers over a broad range of regularization parameters. We observed a trend that task performance remained fairly constant for a range of regularization parameters before decreasing for large amounts of regularization.
Two common regularization methods in reconstruction of magnetic resonance images are total variation (TV) which restricts the magnitude of the gradient in the reconstructed image and wavelet sparsity which assumes that the object being imaged is sparse in the wavelet domain. These regularization methods have resulted in images with fewer undersampling artifacts and less noise but introduce their own artifacts. In this work, we extend previous results on modeling of human observer performance for images using TV regularization to also predict human detection performance using wavelet regularization and a combination of wavelet and TV regularization. Small lesions were placed in the coil k-space data for fluid-attenuated inversion recovery (FLAIR) brain images from the fastMRI database. The data was undersampled using an acceleration factor of 3.48. The undersampled data was reconstructed using a range of regularization parameters for both the TV and wavelet regularization. The internal noise level for the sparse difference-of-Gaussians (S-DOG) model observer was chosen to match the average human percent correct in two-alternative forced choice (2-AFC) studies with a signal known exactly with variable backgrounds and no regularization. The S-DOG model largely tracked the human observer results except at large values of the regularization parameter where it outperformed the average human observer. We found that the regularization with either constraint or in combination did not improve human observer performance for this task.
Task-based assessment of image quality in undersampled magnetic resonance imaging (MRI) using constraints is important because of the need to quantify the effect of the artifacts on task performance. Fluid-attenuated inversion recovery (FLAIR) images are used in detection of small metastases in the brain. In this work we carry out two-alternative forced choice (2-AFC) studies with a small signal known exactly (SKE) but with varying background for reconstructed FLAIR images from undersampled multi-coil data. Using a 4x undersampling and a total variation (TV) constraint we found that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. Using the TV constraint did not improve task performance. The non- prewhitening eye (NPWE) observer and sparse difference-of-Gaussians (S-DOG) observer with internal noise were used to model human observer detection. The parameters for the NPWE and the internal noise for the S-DOG were chosen to match the average percent correct (PC) in 2-AFC studies for three observers using no regularization. The NPWE model observer tracked the performance of the human observers as the regularization was increased but slightly over-estimated the PC for large amounts of regularization. The S-DOG model observer with internal noise tracked human performace for all levels of regularization studied. To our knowledge this is the first time that model observers have been used to track human observer detection for undersampled MRI.
Magnetic resonance imaging (MRI) data acquisition is sometimes accelerated by pseudo-random under-sampling of the frequency domain which is followed by constrained reconstruction. This approach to acceleration assumes a certain level of sparsity of the object being imaged. The sparsity is typically considered for the background anatomy but not explored in terms of a signal detection task. In this study we implement a 2.56x one dimensional acceleration in the acquisition using fully sampled low frequencies and randomly sampled high frequencies with a total variation reconstruction. A small and a large lesion were synthetically placed in a 3D MRI volume in non-overlapping regions. From 40 slices of this volume and 16 regions per slice, 640 sub-images with and without signals were generated to estimate the detection performance of lesions with anatomical variation. We compared the effect of this approach on signal detection using a channelized Hotelling observer approximating the ideal linear observer (with 10 Laguerre-Gauss channels) and one approximating a human observer (with sparse difference-of-Gaussians channels). The area under the receiver operating characteristic curve (AUC) was estimated using the Mann-Whitney statistic and the uncertainty of the estimate was assessed using a bootstrap distribution with 10,000 samples. We found that for these two tasks and model observers, total variation did not lead to a statistically significant improvement in detection performance and that the effect of regularization was larger for the Laguerre-Gauss model than for the sparse difference-of-Gaussians model.
A challenge for task-based optimization is the time required for each reconstructed image in applications where reconstructions are time consuming. Our goal is to reduce the number of reconstructions needed to estimate the area under the receiver operating characteristic curve (AUC) of the infinitely-trained optimal channelized linear observer. We explore the use of classifiers which either do not invert the channel covariance matrix or do feature selection. We also study the assumption that multiple low contrast signals in the same image of a non-linear reconstruction do not significantly change the estimate of the AUC. We compared the AUC of several classifiers (Hotelling, logistic regression, logistic regression using Firth bias reduction and the least absolute shrinkage and selection operator (LASSO)) with a small number of observations both for normal simulated data and images from a total variation reconstruction in magnetic resonance imaging (MRI). We used 10 Laguerre-Gauss channels and the Mann-Whitney estimator for AUC. For this data, our results show that at small sample sizes feature selection using the LASSO technique can decrease bias of the AUC estimation with increased variance and that for large sample sizes the difference between these classifiers is small. We also compared the use of multiple signals in a single reconstructed image to reduce the number of reconstructions in a total variation reconstruction for accelerated imaging in MRI. We found that AUC estimation using multiple low contrast signals in the same image resulted in similar AUC estimates as doing a single reconstruction per signal leading to a 13x reduction in the number of reconstructions needed.
The statistical properties of medical images are central in characterizing the performance of imaging systems. The noise
in cone-beam CT (CBCT) is often characterized using Fourier-based metrics, such as the 3D noise-power spectrum
(NPS). Under a stationarity assumption, the NPS provides a complete representation of the covariance of the images,
since the covariance matrix of the Fourier transform of the image is diagonal. In practice, such assumptions are obeyed
to varying degrees. The objective of this work is to investigate the degree to which such assumptions apply in CBCT and
to experimentally characterize the NPS and off-diagonal elements under a range of experimental conditions. A benchtop
CBCT system was used to acquire 3D image reconstructions of various objects (air and a water cylinder) across a range
of experimental conditions that could affect stationarity (bowtie filter and dose). We test the stationarity assumption
under such varying experimental conditions using both spatial and frequency domain measures of stationarity. The
results indicate that experimental conditions affect the degree of stationarity and that under some imaging conditions,
local descriptions of the noise need to be developed to appropriately describe CBCT images. The off-diagonal elements
of the DFT covariance matrix may not always be ignored.
KEYWORDS: 3D modeling, 3D metrology, 3D image processing, Sensors, Imaging systems, Modulation transfer functions, Interference (communication), Systems modeling, Stereoscopy, X-rays
Crucial to understanding the factors that govern imaging performance is a rigorous analysis of signal and noise transfer
characteristics (e.g., MTF, NPS, and NEQ) applied to a task-based performance metric (e.g., detectability index). This
paper advances a theoretical framework for calculation of the NPS, NEQ, and DQE of cone-beam CT (CBCT) and
tomosynthesis based on cascaded systems analysis. The model considers the 2D projection NPS propagated through a
series of reconstruction stages to yield the 3D NPS, revealing a continuum (from 2D projection radiography to limited-angle
tomosynthesis and fully 3D CBCT) for which NEQ and detectability index may be investigated as a function of
any system parameter. Factors considered in the cascade include: system geometry; angular extent of source-detector
orbit; finite number of views; log-scaling; application of ramp, apodization, and interpolation filters; back-projection;
and 3D noise aliasing - all of which have a direct impact on the 3D NEQ and DQE. Calculations of the 3D NPS were
found to agree with experimental measurements across a broad range of imaging conditions. The model presents a
theoretical framework that unifies 3D Fourier-based performance metrology in tomosynthesis and CBCT, providing a
guide to optimization that rigorously considers the system configuration, reconstruction parameters, and imaging task.
Radiology-based lung-cancer detection is a high-contrast imaging task, consisting of the detection of a small mass of tissue within much lower density lung parenchyma. This imaging task requires removal of confounding image details, fast image acquisition (< 0.1 s for pericardial region), low dose (comparable to a chest x-ray), high resolution (< 0.25 mm in-plane) and patient positioning flexibility. We present an investigation of tomosynthesis, implemented using the Scanning-Beam Digital X-ray System (SBDX), to achieve these goals. We designed an image-based computer model of tomosynthesis using a high-resolution (0.15-mm isotropic voxels), low-noise CT volume image of a lung phantom, numerically added spherical lesions and convolution-based tomographic blurring. Lesion visibility was examined as a function of half-tomographic angle for 2.5 and 4.0 mm diameter lesions. Gaussian distributed noise was added to the projected images. For lesions 2.5 mm and 4.0 mm in diameter, half-tomographic angles of at least 6° and 9° respectively were necessary before visualization of the lesions improved. The addition of noise for a dose equivalent to 1/10 that used for a standard chest radiograph did not significantly impair lesion detection. The results are promising, indicating that lung-cancer detection using a modified SBDX system is possible.
KEYWORDS: Signal to noise ratio, Radiography, Imaging systems, Signal detection, Data modeling, Photons, Sensors, Interference (communication), Modulation transfer functions, Analog electronics
Currently, there is significant interest in quantifying the performance of digital radiography systems. Digital radiography systems can be thought of as continuous linear shift-invariant systems followed by sampling. This view, along with the large number of pixels used for flat-panel systems, has motivated much of the work which attempts to extend figures of merit developed for analog systems, in particular, the detective quantum efficiency (DQE) and the noise equivalent quanta (NEQ). A more general approach looks at the system as a continuous-to-discrete mapping and evaluates the signal-to-noise ratio (SNR) completely from the discrete data. In this paper, we study the effect of presampling blur on these figures of merit. We find that even in this idealized model the DQE/NEQ formulations do not accurately track the behavior of the fully digital SNR. Therefore, DQE/NEQ cannot be viewed as indicators of the signal-known-exactly/background-known-exactly (SKE/BKE) detectability. In order to make design decisions by optimizing detectability one must work with the fully digital definition of detectability.
KEYWORDS: Sensors, X-ray detectors, Signal to noise ratio, Fourier transforms, Signal processing, Digital signal processing, Signal detection, Imaging systems, Medical imaging, Convolution
The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.
We apply task-based assessment of image quality to optical tomography imaging systems. In particular, we studied the task of detecting a signal, specified as a change in scattering and absorption coefficients, when its shape and location were known. The detectability was quantified using the optimal linear (Hotelling) observer. The non-linearity of the problem was no impediment in computing the Hotelling observer using a hybrid approach that combines knowledge of the measurement statistics with sampling to account for anatomical variation. We compared the observer performance on the raw data in uniform and structured backgrounds for several data and signal types. Two of the data types studied were the total number of photons (total counts) collected for each source-detector pair and their respective mean time of arrival. Results show that the spatial variation of detectability was different for the total counts than for the mean time. The performance of the total counts and its relative performance to the mean time varied significantly with both signal type and background variations.
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