nils-herrmann/clean_scirepeval huggingface dataset:
Fast Variance Prediction for Iteratively Reconstructed CT Images With Locally Quadratic Regularization

Predicting noise properties of iteratively reconstructed CT images is useful for analyzing reconstruction methods; for example, local noise power spectrum (NPS) predictions may be used to quantify the detectability of an image feature, to design regularization methods, or to determine dynamic tube current adjustment during a CT scan. This paper presents a method for fast prediction of reconstructed image variance and local NPS for statistical reconstruction methods using quadratic or locally quadratic regularization. Previous methods either require impractical computation times to generate an approximate map of the variance of each reconstructed voxel, or are restricted to specific CT geometries. Our method can produce a variance map of the entire image, for locally shift-invariant CT geometries with sufficiently fine angular sampling, using a computation time comparable to a single back-projection. The method requires only the projection data to be used in the reconstruction, not a reconstruction itself, and is reasonably accurate except near image edges where edge-preserving regularization behaves highly nonlinearly. We evaluate the accuracy of our method using reconstructions of both simulated CT data and real CT scans of a thorax phantom.
An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms

The majorize-minimize (MM) optimization technique has received considerable attention in signal and image processing applications, as well as in statistics literature. At each iteration of an MM algorithm, one constructs a tangent majorant function that majorizes the given cost function and is equal to it at the current iterate. The next iterate is obtained by minimizing this tangent majorant function, resulting in a sequence of iterates that reduces the cost function monotonically. A well-known special case of MM methods are expectation-maximization algorithms. In this paper, we expand on previous analyses of MM, due to Fessler and Hero, that allowed the tangent majorants to be constructed in iteration-dependent ways. Also, this paper overcomes an error in one of those earlier analyses. There are three main aspects in which our analysis builds upon previous work. First, our treatment relaxes many assumptions related to the structure of the cost function, feasible set, and tangent majorants. For example, the cost function can be nonconvex and the feasible set for the problem can be any convex set. Second, we propose convergence conditions, based on upper curvature bounds, that can be easier to verify than more standard continuity conditions. Furthermore, these conditions allow for considerable design freedom in the iteration-dependent behavior of the algorithm. Finally, we give an original characterization of the local region of convergence of MM algorithms based on connected (e.g., convex) tangent majorants. For such algorithms, cost function minimizers will locally attract the iterates over larger neighborhoods than typically is guaranteed with other methods. This expanded treatment widens the scope of the MM algorithm designs that can be considered for signal and image processing applications, allows us to verify the convergent behavior of previously published algorithms, and gives a fuller understanding overall of how these algorithms behave.
New complete-data spaces and faster algorithms for penalized-likelihood emission tomography

The classical expectation-maximization (EM) algorithm for image reconstruction suffers from particularly slow convergence when additive background effects such as accidental coincidences and scatter are included. In addition, when smoothness penalties are included in the objective function, the M-step of the EM algorithm becomes intractable due to parameter coupling. The authors describe the space-alternating generalized EM (SAGE) algorithm, in which the parameters are updated sequentially using a sequence of small "hidden" data spaces rather than one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. By choosing hidden-data spaces with considerably less Fisher information than the conventional complete-data space for Poisson data, the authors obtain significant improvements in convergence rate. This acceleration is due to statistical considerations, not to numerical overrelaxation methods, so monotonic increases in the objective function and global convergence are guaranteed. Due to the space constraints, the authors focus on the unpenalized case in this summary, and they eliminate derivations that are similar to those in Lange and Carson,  Tomography, vol. 8, no. 2, p.306-16 (1984).<<ETX>>
Accelerated dual gradient-based methods for total variation image denoising/deblurring problems

We study accelerated dual gradient-based methods for image denoising/deblurring problems based on the total variation (TV) model. For the TV-based denoising problem, combining the dual approach and Nesterov's fast gradient projection (FGP) method has been found effective. The corresponding denoising method minimizes the dual function with FGP's optimal rate O(1/k2) where k denotes the number of iterations, and guarantees a rate O(1/k) for the primal function decrease. Considering that the dual projected gradient decrease is closely related to the primal function decrease, this paper proposes new accelerated gradient projection methods that decrease the projected gradient norm with a fast rate O(1/k1.5) and that are as efficient as FGP. The proposed approach also decreases the primal function with a faster rate O(1/k1.5). We provide preliminary results on image denoising/deblurring problems with a TV regularizer, where the fast and efficient denoising solver is iteratively used for solving a deblurring problem as the inner proximal update of a fast iterative shrinkage/thresholding algorithm (FISTA).
On complete-data spaces for PET reconstruction algorithms

As investigators consider more comprehensive measurement models for emission tomography, there will be more choices for the complete-data spaces of the associated expectation-maximization algorithms for maximum-likelihood estimation. It is shown that EM algorithms based on smaller complete-data spaces will typically converge faster. Two practical applications of these concepts are discussed: the ML-IA and ML-IB image reconstruction algorithms of D.G. Politte and D.L. Snyder (1991) which are based on measurement models that account for attenuation and accidental coincidences in positron emission tomography (PET); and the problem of simultaneous estimation of emission and transmission parameters. Although the PET applications may often violate the necessary regularity conditions, the authors' analysis predicts heuristically that the ML-IB algorithm, which has a smaller complete-data space, should converge faster than ML-IA.
Optimizing MR Scan Design for Model-Based ${T}_{1}$ , ${T}_{2}$ Estimation From Steady-State Sequences.

Rapid, reliable quantification of MR relaxation parameters T1 and T2 is desirable for many clinical applications. Steady-state sequences such as Spoiled Gradient-Recalled Echo (SPGR) and Dual-Echo Steady-State (DESS) are fast and well-suited for relaxometry because the signals they produce are quite sensitive to T1 and T2 variation. However, T1, T2 estimation with these sequences typically requires multiple scans with varied sets of acquisition parameters. This paper describes a systematic framework for selecting scan types (e.g., combinations of SPGR and DESS scans) and optimizing their respective parameters (e.g., flip angles and repetition times). The method is based on a Cramér-Rao Bound (CRB)-inspired min-max optimization that finds scan parameter combinations that robustly enable precise object parameter estimation. We apply this technique to optimize combinations of SPGR and DESS scans for T1, T2 relaxometry in white matter (WM) and grey matter (GM) regions of the human brain at 3T field strength. Phantom accuracy experiments show that SPGR/DESS scan combinations are in excellent agreement with reference measurements. Phantom precision experiments show that trends in T1,T2 pooled sample standard deviations reflect CRB-based predictions. In vivo experiments show that in WM and GM, T1 and T2 estimates from a pair of optimized DESS scans exhibit precision (but not necessarily accuracy) comparable to that of optimized combinations of SPGR and DESS scans. To our knowledge, T1 maps from DESS acquisitions alone are new. This example application illustrates that scan optimization may help reveal new parameter mapping techniques from combinations of established pulse sequences.
Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs

This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.
Statistical reconstruction for quantitative CT applications

This paper summarizes considerations in developing statistical reconstruction algorithms for polyenergetic X-ray CT. The algorithms are based on Poisson statistics and polyenergetic X-ray attenuation physics and object models. In single-kVp scans, object models enable estimates of the contributions of bone and soft tissue at every pixel, based on prior assumptions about the tissue properties. In dual-kVp scans, one can estimate water and bone images independently. Preliminary results with fan-beam data from two cone beam systems show better accuracy for iterative methods over FBP.
Update on HE vs UHE collimation for focal total-activity quantification in I-131 SPECT using 3D OSEM

We calibrated a scintillation camera for the counts-to-activity conversion factor, CF, by measuring a phantom consisting of a sphere containing a known 131-I activity placed within an elliptical cylinder. Within a 3D OSEM reconstruction algorithm, we employed a depth-dependent detector-response model based on smooth fits to the point-source-response function. Using the ultra-high-energy (UHE) collimator and 100 iterations, the recovery coefficient, RC, appeared to be 1 for any sphere volume down to 20 cm/sup 3/. The CF changed only a small amount as the background-over-target activity concentration ratio, b, increased for both UHE and high-energy (HE) collimation. Tests of activity quantification were carried out with an anthropomorphic phantom simulating a 100 cm/sup 3/ spherical tumor centrally located inferior to the lungs. With 3D OSEM reconstruction, using the global-average CF and no RC-based correction, mean bias in the simulated-tumor activity estimate over 20 realizations was -7.4% with UHE collimation, and -9.4% with HE collimation. For comparison, with 1D SAGE reconstruction, using the CF corresponding to the experimental estimate of b and RC-based correction, the mean bias was worse, -10.7% for UHE collimation, but better, -4.3 %, for HE collimation.
Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches [based on Stein's unbiased risk estimate (SURE)] need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: predicted-SURE and projected-SURE (which require knowledge of noise variance σ2), and GCV (which does not need σ2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation and an analysis-type ℓ1-regularization. We demonstrate through simulations and experiments with real data that minimizing predicted-SURE and projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observe that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly suboptimal for MRI. Theoretical derivations in this paper related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms.
Accelerated ordered-subsets algorithm based on separable quadratic surrogates for regularized image reconstruction in X-ray CT

Iterative algorithms for X-ray CT image reconstruction offer the possibility of reduced dose and/or improved image quality, but require substantial compute time. Reducing the time will likely require algorithms that can be massively parallelized. Ordered subsets (OS) algorithms update all voxels simultaneously and thus are amenable to such parallelization. We present an new monotonic algorithm for regularized image reconstruction that is derived using optimization transfer with separable quadratic surrogates (SQS). The new algorithm accelerates the convergence rate by adapting reduced curvature values for the regularizer that were proposed by Yu et al.  for coordinate descent algorithms. We further accelerate the algorithm using ordered subsets. Simulation results show that the proposed OS algorithm converges faster than the traditionalOS algorithmforX-ray CT reconstruction from a limited number of projection views.
Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms

Iterative coordinate ascent algorithms have been shown to be useful for image recovery, but are poorly suited to parallel computing due to their sequential nature. This paper presents a new fast converging parallelizable algorithm for image recovery that can be applied to a very broad class of objective functions. This method is based on paraboloidal surrogate functions and a concavity technique. The paraboloidal surrogates simplify the optimization problem. The idea of the concavity technique is to partition pixels into subsets that can be updated in parallel to reduce the computation time. For fast convergence, pixels within each subset are updated sequentially using a coordinate ascent algorithm. The proposed algorithm is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints. A global convergence proof is summarized. Simulation results show that the proposed algorithm requires less elapsed time for convergence than iterative coordinate ascent algorithms. With four parallel processors, the proposed algorithm yields a speedup factor of 3.77 relative to single processor coordinate ascent algorithms for a three-dimensional (3-D) confocal image restoration problem.
Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.
Channelized hotelling observer performance for penalized-likelihood image reconstruction

What type of regularization method is optimal for penalized-likelihood image reconstruction when the imaging task is signal detection based on a channelized Hotelling (CHO) observer? To answer such questions, one would like to have a simple analytical expression (even if approximate) for the performance (SNR) of the CHO observer given different reconstruction methods. Bonetto, Qi, and Leahy (IEEE T-NS, Aug. 2000) derived and validated one such expression for penalized-likelihood (aka MAP) reconstruction and the Signal Known Exactly (SKE) problem using linearizations and local shift-invariance approximations. This paper describes a further simplification of the analytical SNR expression for the more general case of a Gaussian-distributed signal. This simplification, based on frequency-domain decompositions, greatly reduces computation time and thus can facilitate analytical comparisons between reconstruction methods in the context of detection tasks. It also leads to the very interesting result that regularization is not essential in this context for a large family of linear observers.
Incremental optimization transfer algorithms: application to transmission tomography

No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters (Ahn and Fessler, 2003), and methods based on the incremental expectation maximization (EM) approach (Hsiao et al., 2002). This paper generalizes the incremental EM approach by introducing a general framework that we call ¿incremental optimization transfer.¿ Like incremental EM methods, the proposed algorithms accelerate convergence speeds and ensure global convergence (to a stationary point) under mild regularity conditions without requiring inconvenient relaxation parameters. The general optimization transfer framework enables the use of a very broad family of non-EM surrogate functions. In particular, this paper provides the first convergent OS-type algorithm for transmission tomography. The general approach is applicable to both monoenergetic and polyenergetic transmission scans as well as to other image reconstruction problems. We propose a particular incremental optimization transfer method for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS). Results show that the new ¿transmission incremental optimization transfer (TRIOT)¿ algorithm is faster than nonincremental ordinary SPS and even OS-SPS yet is convergent.
Globally convergent algorithms for maximum a posteriori transmission tomography

This paper reviews and compares three maximum likelihood algorithms for transmission tomography. One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro (see  1993) in the context of emission tomography, and one is an ad hoc gradient algorithm. The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors. Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm. This superiority stems from the larger number of exponentiations required by the EM algorithm. The convex and gradient algorithms are well adapted to parallel computing.
Improved modeling of system response in list mode EM reconstruction of Compton scatter camera images

An improved List Mode EM method for reconstructing Compton scattering camera images has been developed. First, an approximate method for computation of the spatial variation in the detector sensitivity has been derived and validated by Monte Carlo computation. A technique for estimating the relative weight of system matrix coefficients for each gamma in the list has also been employed, as has a method for determining the relative probabilities of emission having some from pixels tallied in each list-mode back-projection. Finally, a technique has been developed for modeling the effects of Doppler broadening and finite detector energy resolution on the relative weights for pixels neighbor to those intersected by the back-projection, based on values for the FWHM of the spread in the cone angle computed by Monte Carlo. Memory issues typically associated with list mode reconstruction are circumvented by storing only a list of the pixels intersected by the back-projections, and computing the weights of the neighboring pixels at each iteration step. Simulated projection data has been generated for a representative Compton camera system (CSPRINT) for several source distributions and reconstructions performed. Reconstructions have also been performed for experimental data for distributed sources.
Quadratic Regularization Design for 2-D CT

Statistical methods for tomographic image reconstruction have improved noise and spatial resolution properties that may improve image quality in X-ray computed tomography (CT). Penalized weighted least squares (PWLS) methods using conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution due to interactions between the weighting, which is necessary for good noise properties, and the regularizer. Previously, we addressed this problem for parallel-beam emission tomography using matrix algebra methods to design data-dependent, shift-variant regularizers that improve resolution uniformity. This paper develops a fast angular integral mostly analytical (AIMA) regularization design method for 2-D fan-beam X-ray CT imaging, for which parallel-beam tomography is a special case. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in transmission tomography when using quadratic regularization.
Uniform quadratic penalties cause nonuniform spatial resolution

Examines the spatial resolution properties of penalized maximum-likelihood image reconstruction methods by analyzing the local impulse response. The authors show that for emission image reconstruction using the ordinary uniform quadratic regularization penalty, the local impulse response is spatially variant. Paradoxically, the local resolution is poorest in high activity regions. The analysis leads naturally to a modified quadratic regularization penalty that achieves nearly uniform resolution. The modified penalty also provides a very practical method for choosing the smoothing parameter to obtain a specified resolution.<<ETX>>