nils-herrmann/clean_scirepeval huggingface dataset:
Simultaneous estimation of attenuation and activity images using optimization transfer

This paper addresses the application of optimization transfer to simultaneous statistical estimation of attenuation and activity images in tomographic Image reconstruction. Although the technique we propose has wider applicability, we focus on the problem of reconstructing from data acquired via a post-injection transmission scan protocol. In this protocol, emission scan data Is supplemented with transmission scan data that is acquired after the patient has received the Injection of radio-tracer. The negative loglikelihood function for this data is a complicated function of the activity and attenuation images, leading to an objective function for the model that is difficult to minimize for the purpose of estimation. Previous work on this problem showed that when either the attenuation or activity image was held fixed, a paraboloidal surrogate could be found for the negative loglikelihood as a function of the remaining variables. This led to an algorithm In which the model's objective function is alternately minimized as a function of the attenuation and activity, using the optimization transfer technique. In the work we present here, however, we develop bivariate surrogates for the loglikelihood, i.e., functions that serve as surrogates with respect to both the attenuation and activity variables. Hence, simultaneous minimization in all variables can be carried out, potentially leading to convergence in fewer surrogate minimizations.
Benefits of position-sensitive detectors for source detection with known background

We address the question of whether or not the directional or imaging information offered by a position-sensitive gamma-ray detector improves the detection accuracy when searching for a source of known shape amid a background of known intensity. We formulate the detection problem as a composite hypothesis testing problem and examine the behavior of the generalized likelihood ratio test (GLRT) in terms of the area under the receiver operating characteristic (AUC). Due to the analytical complexity of the GLRT in this case, we examine its asymptotic properties when the number of detected photons is large. We find that a detector of uniform sensitivity can more accurately detect a source when imaging information is used.
Undersampled Phase Retrieval With Outliers

This paper proposes a general framework for reconstructing sparse images from undersampled (squared)magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1-D Monte Carlo tests and 2-D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.
Penalized weighted least-squares image reconstruction for positron emission tomography

Presents an image reconstruction method for positron-emission tomography (PET) based on a penalized, weighted least-squares (PWLS) objective. For PET measurements that are precorrected for accidental coincidences, the author argues statistically that a least-squares objective function is as appropriate, if not more so, than the popular Poisson likelihood objective. The author proposes a simple data-based method for determining the weights that accounts for attenuation and detector efficiency. A nonnegative successive over-relaxation (+SOR) algorithm converges rapidly to the global minimum of the PWLS objective. Quantitative simulation results demonstrate that the bias/variance tradeoff of the PWLS+SOR method is comparable to the maximum-likelihood expectation-maximization (ML-EM) method (but with fewer iterations), and is improved relative to the conventional filtered backprojection (FBP) method. Qualitative results suggest that the streak artifacts common to the FBP method are nearly eliminated by the PWLS+SOR method, and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over FBP.
A min-max approach to the multidimensional nonuniform FFT: application to tomographic image reconstruction

The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents a method for the nonuniform FT that is optimal in a min-max sense. The proposed method minimizes the worst-case approximation error over all signals of unit norm. Unlike many previous methods for the nonuniform FT, the proposed method easily generalizes to multidimensional signals. We are investigating this method as a fast algorithm for computing the Radon transform in 2D iterative tomographic image reconstruction.
Model-based reconstruction of spectral and spatial source distribution from objects with known motion

A model-based activity reconstruction in both the energy and spatial domains is developed that includes separate parameterization for any objects moving with known motion. This approach corrects for object motion, without smearing the stationary backdrop space. The goal is to simultaneously obtain an energy-dependent spatial map of the radiation field for the backdrop and for each parameterized moving object. Experimental results show that the method can successfully reconstruct the activity of moving objects while also revealing stationary sources in the backdrop. Also, by including the possibility of partial photon energy deposition in the detector in the model, the incident energy spectrum is reconstructed more accurately.
Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms.
Penalized likelihood emission image reconstruction with uncertain boundary information

In this paper, a method is introduced for incorporating perfectly registered MRI boundary information into a penalized likelihood emission reconstruction scheme. The boundary curve is modeled as a periodic spline whose coefficients are estimated from the MRI image. The resulting boundary estimate is mapped to a spatially variant set of Gibbs weights. When incorporated into a quadratic roughness penalty, these weights improve emission reconstruction bias/variance performance by preventing smoothing across the estimated boundary. Finally, we derive a new penalty function that accounts for the uncertainty inherent in the boundary estimates.
Sure-based parameter selection for parallel MRI reconstruction using GRAPPA and sparsity

New methods have been developed for parallel MRI reconstruction combining GRAPPA and sparsity. One impediment to the practical application of such methods is selecting a regularization parameter that acceptably balances the contributions of GRAPPA and sparsity. We propose a broadly applicable Monte-Carlo-based approximation to Stein's unbiased risk estimate (SURE) for a suitable weighted mean-squared error (WMSE) metric. Applying this approximation to predict the WMSE-optimal tuning parameter for sparsity-based reconstruction, we are able to tune our parameter to achieve nearly MSE-optimal performance. In our simulations, we vary the noise level in the simulated data and use our Monte-Carlo method to tune the reconstruction to the noise level automatically.
Exploring estimator bias-variance tradeoffs using the uniform CR bound

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an "unachievable region" of the delta-sigma plane for a specified statistical model. In order to place an estimator on this plane for comparison with the delta-sigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log-likelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems.
Objective functions for tomographic reconstruction from randoms-precorrected PET scans

In PET, usually the data are precorrected for accidental coincidence (AC) events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for AC events but destroys the Poisson statistics. Furthermore, for transmission tomography the weighted least-squares (WLS) method leads to systematic biases, especially at low count rates. We propose a new "shifted" Poisson (SP) model for precorrected PET data, which properly matches the first and second order moments of the measurement statistics. Using simulations and analytic approximations, we show that estimators based on the "ordinary" Poisson (OF) model for the precorrected data lead to higher standard deviations than the proposed method. Moreover, if one zero-thresholds the data before applying the maximization algorithm, the OP model results in systematic bias. It is shown that the proposed SP model leads to penalized-likelihood estimates free of systematic bias, even for zero-thresholded data. The proposed SP model does not increase the computation requirements compared to OP model and it is robust to errors in the estimates of the AC event rates.
Preliminary studies on the feasibility of addition of vertex view to conventional brain SPECT

We have investigated the improvement in resolution and sensitivity for brain imaging which would result by the addition of a single stationary vertex view to the tomographic data. This method has the practical advantage of being relatively inexpensive and easy to implement. The uniform Cramer Rao bound is a plot of the minimum achievable standard deviation for estimating the pixel intensity as a function of the bias gradient length. Uniform CR bound analysis indicated an improvement in performance when the vertex detector is added, especially for centrally located pixels for which improvement is seen over the useful depth for brain imaging. Simulation experiments were done with a simple six slice phantom and with the Hoffman brain phantom. Visual inspection of the reconstructed images showed improved resolution and noise characteristics over reconstructed images without the vertex data. Quantitatively, substantial reduction in mean square error was observed for a plane close to the vertex detector. Improvement reduced as distance from the vertex detector is increased. Background activities inside the field of view of the vertex detector but not the tomograph were represented by several blobs of activity on a plane lying outside the reconstruction volume. This activity was estimated by 3D spline fitting jointly with the image reconstruction process. Adding the vertex view to conventional brain SPECT should lead to improved cortical imaging, and to moderate improvement for deep structures.
Quadratic Regularization Design for Iterative Reconstruction in 3D multi-slice Axial CT

In X-ray CT, statistical methods for tomographic image reconstruction create images with better noise properties than conventional filtered back projection (FBP) techniques. Penalized-likelihood (PL) image reconstruction methods maximize an objective function based on the log-likelihood of sinogram measurements and on a user defined roughness penalty which controls noise. Penalized-likelihood methods (as well as penalized weighted least squares methods) based on conventional quadratic regularizers result in nonuniform and anisotropic spatial resolution. We have previously addressed this problem for 2D emission tomography, 2D fan-beam transmission tomography, and 3D cylindrical emission tomography. This paper extends those methods to 3D multi-slice axial CT with small cone angles.
Efficient calculation of resolution and covariance for penalized-likelihood reconstruction in fully 3-D SPECT

Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.
Unbiased Filtered Back-Projection in $4\pi$ Compton Imaging With 3D Position Sensitive Detectors

In Compton imaging, iterative methods provide good performance but are usually computationally intensive. Thus, direct inverse algorithms such as filtered back-projection (FBP) are preferable when computation time is limited. The conventional FBP method assumes that the point spread function of a back-projection image is isotropic and invariant to incident direction, as required by frequency spectrum analysis. However, most of the time this assumption is not true because the detector geometry is rarely uniform. Therefore the conventional FBP reconstructed image is biased. To solve the geometry non-uniformity problem, this paper proposes an unbiased FBP algorithm that groups Compton events having the same Compton rings using a system matrix decomposition strategy. The proposed method produces more isotropic resolution, and preserves the capability to use frequency spectrum analysis. The algorithm has been applied to data from a 3D position-sensitive detector array with 4 crystals and a digital readout system. The resulting images had more isotropic resolution than standard FBP.
Fully 3D PET image reconstruction using a Fourier preconditioned conjugate-gradient algorithm

Since the data sixes in fully 3D PET imaging are very large, iterative image reconstruction algorithms must converge in very few iterations to be useful. One can improve the convergence rate of the conjugate-gradient (CG) algorithm by incorporating preconditioning operators that approximate the inverse of the Hessian of the objective function. If the 3D cylindrical PET geometry were not truncated at the ends, then the Hessian of the penalized least-squares objective function would be approximately shift-invariant, i.e. G'G would be nearly block-circulant, where G is the system matrix. The authors propose a Fourier preconditioner based on this shift-invariant approximation to the Hessian. Results show that this preconditioner significantly accelerates the convergence of the CG algorithm with only a small increase in computation.
Spatial Resolution Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.
A paraboloidal surrogates algorithm for convergent penalized-likelihood emission image reconstruction

We present a new algorithm for penalized-likelihood emission image reconstruction. The algorithm monotonically increases the objective function, converges globally to the unique maximizer, and easily accommodates the nonnegativity constraint and nonquadratic but convex penalty functions. The algorithm is based on finding paraboloidal surrogate functions for the log-likelihood at each iteration: quadratic functions that are tangent to the log-likelihood at the current image estimate, and lie below the log-likelihood over the entire nonnegative orthant. These conditions ensure monotonicity. The paraboloidal surrogates are maximized easily using existing algorithms such as coordinate ascent. Simulation results show that the proposed algorithm converges faster than the SAGE algorithm, yet the new algorithm is somewhat easier to implement.
Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms

Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.
Fast Monotonic Algorithms for Transmission Tomography

We present a framework for designing fast and monotonic algorithms for transmission tomography penalized-likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log likelihood. Due to the form of the log-likelihood function it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log likelihood that arises due to background events, such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified at each iteration, the CPU time is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity, and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real and simulated PET transmission scans.
REGULARIZED B1+ MAP ESTIMATION IN MRI

A challenge in MR imaging is that RF transmit coils produce non-uniform field strengths, so an excitation pulse will produce tip angles that vary substantially from the desired tip angle over the field of view. For parallel transmit excitation (using a coil array), it is important to have a map of the B1+ field strength (and phase) for RF pulse design. Standard B1+ map estimation methods perform poorly in image regions with low spin density. This paper describes a regularized method for B1+ map estimation using MR scans for each coil and for two or more tip angles. Using these scans and exploiting the fact that maps are generally smooth, the iterative algorithm estimates both the magnitude and phase at each coil's B1+ map. Results from both simulations and real MR data show significant improvements over conventional unregularized methods for B1 + mapping.