nils-herrmann/clean_scirepeval huggingface dataset:
Regularized Field Map Estimation in MRI

In fast magnetic resonance (MR) imaging with long readout times, such as echo-planar imaging (EPI) and spiral scans, it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring. Such corrections require an accurate field map, a map of the off-resonance frequency at each voxel. Standard field map estimation methods yield noisy field maps, particularly in image regions with low spin density. This paper describes regularized methods for field map estimation from two or more MR scans having different echo times. These methods exploit the fact that field maps are generally smooth functions. The methods use algorithms that decrease monotonically a regularized least-squares cost function, even though the problem is highly nonlinear. Results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods.
Iterative image reconstruction for dual-energy X-ray CT using regularized material sinogram estimates

X-ray CT images have various applications, including CT-based attenuation correction (CTAC) for PET. Low-dose CT imaging is particularly desirable for CTAC. Dual-energy (DE) CT imaging methods may improve the accuracy of attenuation correction in PET. However, conventional DE CT approaches to sinogram material decomposition use logarithmic transforms that are sensitive to noise in low-dose scans. This paper describes a DE reconstruction method based on statistical models that avoids using a logarithm. We first estimate material sinograms directly from the raw DE data (without any logarithm), with mild regularization to control noise and avoid outliers. We then apply a penalized weighted least squares (PWLS) method to reconstruct images of the two material components. We also propose a joint edge-preserving regularizer that uses the prior knowledge that the two material images have many region edges located in the same positions. Preliminary simulation results suggest that this iterative method improves image quality compared to conventional approaches based on log data for low-dose DE CT scans.
Moments of implicitly defined estimators (e.g. ML and MAP): applications to transmission tomography

Many estimators in signal processing problems are defined implicitly as the maximum of an objective function, such as maximum likelihood (ML) and maximum a posteriori (MAP) methods. Exact analytical expressions for the mean and variance of such estimators are usually unavailable, so investigators usually resort to numerical simulations. The paper describes approximate analytical expressions for the mean and variance of implicitly defined estimators. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. The authors demonstrate the utility and accuracy of the approximations in a PET transmission computed tomography application with Poisson statistics. The approximations should be useful in a wide range of estimation problems.
Maximum likelihood emission image reconstruction for randoms-precorrected PET scans

Most PET scans are compensated for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences. Real time subtraction of delayed coincidences compensates for the average of AC events, but also destroys the Poisson statistics. Moreover, negative values result during the real-time subtraction which would cause conventional penalized maximum likelihood algorithms to diverge, and setting these negative values to zero introduces a systematic positive bias. The authors have previously developed and compared two new methods for reconstructing transmission scans from randoms precorrected measurements: one based on a "shifted Poisson" (SP) model, and the other based on saddle-point (SD) approximations. Simulations and experimental phantom studies of transmission scans showed that both SP and SD methods lead to significantly lower variance than the conventional maximum likelihood methods (based on the ordinary Poisson (OF) model). The authors have now extended these methods to emission scans. In situations like 3D PET emission scans (with low counts per ray but many total counts and high randoms rates), they show that the proposed methods not only avoid the systematic positive bias of OP method but also lead to significantly lower variance. The new methods offer improved image reconstruction in PET through more realistic statistical modeling, yet with negligible increase in computation over the conventional OP method.
Correction for Collimator-Detector Response in SPECT Using Point Spread Function Template

Compensating for the collimator-detector response (CDR) in SPECT is important for accurate quantification. The CDR consists of both a geometric response and a septal penetration and collimator scatter response. The geometric response can be modeled analytically and is often used for modeling the whole CDR if the geometric response dominates. However, for radionuclides that emit medium or high-energy photons such as I-131, the septal penetration and collimator scatter response is significant and its modeling in the CDR correction is important for accurate quantification. There are two main methods for modeling the depth-dependent CDR so as to include both the geometric response and the septal penetration and collimator scatter response. One is to fit a Gaussian plus exponential function that is rotationally invariant to the measured point source response at several source-detector distances. However, a rotationally-invariant exponential function cannot represent the star-shaped septal penetration tails in detail. Another is to perform Monte-Carlo (MC) simulations to generate the depth-dependent point spread functions (PSFs) for all necessary distances. However, MC simulations, which require careful modeling of the SPECT detector components, can be challenging and accurate results may not be available for all of the different SPECT scanners in clinics. In this paper, we propose an alternative approach to CDR modeling. We use a Gaussian function plus a 2-D B-spline PSF template and fit the model to measurements of an I-131 point source at several distances. The proposed PSF-template-based approach is nearly non-parametric, captures the characteristics of the septal penetration tails, and minimizes the difference between the fitted and measured CDR at the distances of interest. The new model is applied to I-131 SPECT reconstructions of experimental phantom measurements, a patient study, and a MC patient simulation study employing the XCAT phantom. The proposed model yields up to a 16.5 and 10.8% higher recovery coefficient compared to the results with the conventional Gaussian model and the Gaussian plus exponential model, respectively.
A mixture-site model for edge-preserving image restoration

The paper summarizes a new Bayesian method for edge-preserving image restoration from noisy measurements. The line-site method of Geman and Geman (1984) forces region boundaries to lie along pixel boundaries, which is unnatural, particularly for 3D data. The present authors augment the intensity process with a binary "mixture site" process, which has one parameter for each pixel indicating the presence of a boundary at some unknown location within that pixel. The method was motivated by the PET and SPECT transmission images with partial volume effects, and is easily extended to 3D data sets.<<ETX>>
Cramér Rao bound analysis of joint B1/T1 mapping methods in MRI

In MRI, RF field inhomogeneity (B<inf>1</inf>) and relaxation effects (T<inf>1</inf>) significantly affect both B<inf>1</inf> and T<inf>1</inf> mapping. Simultaneous joint estimation of both B<inf>1</inf> and T<inf>1</inf> has the potential to greatly improve both B<inf>1</inf> and T<inf>1</inf> estimation. This paper analyzes the Cramér Rao Bound for joint B<inf>1</inf>, T<inf>1</inf> estimation using common B<inf>1</inf> and T<inf>1</inf> pulse sequences. This analysis aids choosing pulse sequences and parameters given desired levels of B<inf>1</inf> and T<inf>1</inf> accuracy and the inherent trade off between the two mappings.
Accelerated methods for low-rank plus sparse image reconstruction

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. Solving for the L and S components is anonsmooth composite convex minimization problem. While current techniques for this model are based on the classical iterative soft thresholding algorithm (ISTA), accelerated methods can be applied to obtain faster rate of convergence of the algorithm. This paper proposes two alternative methods for solving the L+S problem, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other based on the recent proximal optimized gradient method (POGM). Numerical results suggest faster convergence than the traditional ISTA, while preserving its computational simplicity.
Efficient computation of regularized field map estimates in 3D

Estimating the main magnetic field inhomogeneity is important for many magnetic resonance imaging (MRI) techniques. Regularized estimation methods can provide accurate estimates that intrinsically avoid phase wrapping, account for the chemical shift due to fat, and reduce noise. However, these methods require minimizing nonconvex cost functions and existing algorithms are undesirably slow or do not scale to realistic 3D datasets due to memory limitations. This paper proposes a new algorithm that overcomes these limitations. The algorithm adapts the nonlinear conjugate gradient method by incorporating an monotonic line search and efficient iteration-dependent preconditioning. Experiments on multi-echo field map estimation show that our algorithm is competitive with state-of-the-art methods in 2D, and scale successfully to 3D datasets, where current fast methods fail due to memory limitations.
Detection performance prediction for CdZnTe array

The complex system response of 3D position-sensitive gamma-ray detectors complicates the model for the recorded measurements and makes exact expressions for detection performance intractable. This makes source detection performance difficult and expensive to compute. Asymptotic analysis has the potential to simplify detection performance prediction with complex systems and has previously been applied to detection performance prediction with simulated gamma-ray detectors. In this work, we use asymptotic performance prediction methods to predict points on the receiver operating characteristic (ROC) curve for the illustrative task of detecting a Cs-137 source in background with an 18-detector CdZnTe array. We assume that the source position, background spectrum, and background spatial distribution are known. Our results show that the asymptotic performance prediction method accurately predicts the empirically observed performance even with real data recorded with a real system. Our results also characterize the performance of the detector array for the task of source detection. The accuracy and computational efficiency of the asymptotic detection performance prediction method make it a viable alternative to empirical performance evaluation.
Source Detection Performance Prediction for a CdZnTe Array

The complex system response of 3D position-sensitive gamma-ray detectors complicates modeling the recorded measurements and makes exact expressions for detection performance intractable. This makes source detection performance difficult and expensive to compute. Asymptotic analysis has the potential to simplify detection performance prediction with complex systems and has previously been applied to detection performance prediction with simulated gamma-ray detectors. In this work, we use asymptotic performance prediction methods to predict points on the receiver operating characteristic (ROC) curve for the illustrative task of detecting a 137Cs source in background with an 18-detector CdZnTe array. We assume that the source position, source energy, background spectrum, and background spatial distribution are known. Although these assumptions are not always valid in practice, the efficiency of the prediction method makes it attractive for detection system design problems. Our results show that the asymptotic performance prediction method accurately predicts the empirically observed performance with real data recorded with a real system. Our results also characterize the performance of the detector array for the task of source detection. The accuracy and computational efficiency of the asymptotic detection performance prediction method make it a viable alternative to empirical performance evaluation.
Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction

Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of simultaneous iterative reconstruction technique (SIRT), which is of the former type, with a version of separable quadratic surrogates (SQS), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security.
Iterative image reconstruction in MRI with separate magnitude and phase regularization

Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from non-Cartesian k-space samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either unregularized, and therefore sensitive to noise, or have used regularization methods that smooth the complex valued image. These existing methods regularize the real and imaginary components of the image equally. In many MRI applications, including T/sub 2/*-weighted imaging as used in fMRI BOLD imaging, one expects most of the signal information of interest to be contained in the magnitude of the voxel value, whereas the phase values are expected to vary smoothly spatially. This paper proposes separate regularization of the magnitude and phase components, preserving the spatial resolution of the magnitude component while strongly regularizing the phase component. This leads to a non-convex regularized least-squares cost function. We describe a new iterative algorithm that monotonically decreases this cost function. The resulting images have reduced noise relative to conventional regularization methods.
3D Forward and Back-Projection for X-Ray CT Using Separable Footprints

Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.
Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.
Regularized Image Reconstruction Algorithms for Dual-Isotope Myocardial Perfusion SPECT (MPS) Imaging Using a Cross-Tracer Prior

In simultaneous dual-isotope myocardial perfusion SPECT (MPS) imaging, data are simultaneously acquired to determine the distributions of two radioactive isotopes. The goal of this work was to develop penalized maximum likelihood (PML) algorithms for a novel cross-tracer prior that exploits the fact that the two images reconstructed from simultaneous dual-isotope MPS projection data are perfectly registered in space. We first formulated the simultaneous dual-isotope MPS reconstruction problem as a joint estimation problem. A cross-tracer prior that couples voxel values on both images was then proposed. We developed an iterative algorithm to reconstruct the MPS images that converges to the maximum a posteriori solution for this prior based on separable surrogate functions. To accelerate the convergence, we developed a fast algorithm for the cross-tracer prior based on the complete data OS-EM (COSEM) framework. The proposed algorithm was compared qualitatively and quantitatively to a single-tracer version of the prior that did not include the cross-tracer term. Quantitative evaluations included comparisons of mean and standard deviation images as well as assessment of image fidelity using the mean square error. We also evaluated the cross tracer prior using a three-class observer study with respect to the three-class MPS diagnostic task, i.e., classifying patients as having either no defect, reversible defect, or fixed defects. For this study, a comparison with conventional ordered subsets-expectation maximization (OS-EM) reconstruction with postfiltering was performed. The comparisons to the single-tracer prior demonstrated similar resolution for areas of the image with large intensity changes and reduced noise in uniform regions. The cross-tracer prior was also superior to the single-tracer version in terms of restoring image fidelity. Results of the three-class observer study showed that the proposed cross-tracer prior and the convergent algorithms improved the image quality of dual-isotope MPS images compared to OS-EM.
Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction

Fourier-based forward and back-projection methods have the potential to reduce computation demands in iterative tomographic image reconstruction. Interpolation errors are a limitation of conventional Fourier-based projectors. Recently, the min-max optimized Kaiser-Bessel interpolation within the nonuniform fast Fourier transform (NUFFT) approach has been applied in parallel-beam image reconstruction, whose results show lower approximation errors than conventional interpolation methods. However, the extension of min-max NUFFT approach to fan-beam data has not been investigated. We have extended the min-max NUFFT framework to the fan-beam tomography case, using the relationship between the fan-beam projections and corresponding projections in parallel-beam geometry. Our studies show that the fan-beam Fourier-based forward and back-projection methods can significantly reduce the computation time while still providing comparable accuracy as their space-based counterparts.
Combined diagonal/Fourier preconditioning methods for image reconstruction in emission tomography

Iterative methods for tomographic image reconstruction often converge slowly. Preconditioning methods can often accelerate gradient-based iterations. Previous preconditioning methods for PET reconstruction have used either diagonal or Fourier-based preconditioners. Fourier-based preconditioners are well suited to problems with near-circulant Hessian matrices. However, due to the nonuniform Poisson noise variance in PET, the circulant approximation to the Hessian is suboptimal. This paper shows that a particular combined diagonal/Fourier preconditioner yields a more accurate approximation to the Hessian and gives significantly faster convergence rates than does either preconditioner used alone.
Spectral analysis using regularized non-negative least-squares estimation [positron emission tomography]

The implementation of spectral analysis techniques involves solving a highly underdetermined linear system equation and is prone to the effect of measurement noise. The authors propose to use a regularized non-negative least-square estimator to stabilize the implementation of the technique. They introduce a penalty term in their formulation of the function to discourage disparities in tracer kinetics between neighboring pixels and use an iterative method to impose positivity constraints. The authors show results from analysis of FDG thorax images of patients suspected to have cancers and summarize their findings.
Fast Joint Reconstruction of Dynamic  $R_2^*$ and Field Maps in Functional MRI

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) is conventionally done by reconstructing T<sub>2</sub> <sup>*</sup> -weighted images. However, since the images are unitless they are nonquantifiable in terms of important physiological parameters. An alternative approach is to reconstruct R<sub>2</sub> <sup>*</sup> maps which are quantifiable and have comparable BOLD contrast as T2* -weighted images. However, conventional R<sub>2</sub> <sup>*</sup> mapping involves long readouts and ignores relaxation during readout. Another problem with fMRI imaging is temporal drift/fluctuations in off-resonance. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any temporal changes. Here, we propose a new fast regularized iterative algorithm that jointly reconstructs R<sub>2</sub> <sup>*</sup> and field maps for all time frames in fMRI data. To accelerate the algorithm we linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both R<sub>2</sub> <sup>*</sup> and field maps and provide uniform spatial resolution. For fMRI data with the same temporal frame rate as data collected for T<sub>2</sub> <sup>*</sup> -weighted imaging the resulting R<sub>2</sub> <sup>*</sup> maps performed comparably to T<sub>2</sub> <sup>*</sup> -weighted images in activation detection while also correcting for spatially global and local temporal changes in off-resonance.