nils-herrmann/clean_scirepeval huggingface dataset:
Convergent convolutional dictionary learning using Adaptive Contrast Enhancement (CDL-ACE): Application of CDL to image denoising

Convolutional dictionary learning (CDL) has great potential to “learn” rich sparse representations from training datasets, by training translation-invariant filters. However, the performance of applying learned filters from CDL to inverse problems has not yet been fully maximized because training data preprocessing in training stage is not fully compensated in testing stage. We propose CDL using Adaptive Contrast Enhancement (CDL-ACE) that additionally models the preprocessing in CDL, and image denoising model using learned filters from CDL-ACE. For CDL-ACE, we apply a practically feasible and convergent Block Proximal Gradient method using Majorizer (BPG-M) with a momentum coefficient formula and an adaptive restarting rule. Numerical experiments show that, for strong additive white Gaussian noise, the proposed image denoiser using learned filters by CDL outperforms existing image denoising methods using Wiener filtering and total variation; and learned filters by CDL-ACE further improves the denoiser.
Fast X-Ray CT Image Reconstruction Using a Linearized Augmented Lagrangian Method With Ordered Subsets

Augmented Lagrangian (AL) methods for solving convex optimization problems with linear constraints are attractive for imaging applications with composite cost functions due to the empirical fast convergence rate under weak conditions. However, for problems such as X-ray computed tomography (CT) image reconstruction, where the inner least-squares problem is challenging and requires iterations, AL methods can be slow. This paper focuses on solving regularized (weighted) least-squares problems using a linearized variant of AL methods that replaces the quadratic AL penalty term in the scaled augmented Lagrangian with its separable quadratic surrogate function, leading to a simpler ordered-subsets (OS) accelerable splitting-based algorithm, OS-LALM. To further accelerate the proposed algorithm, we use a second-order recursive system analysis to design a deterministic downward continuation approach that avoids tedious parameter tuning and provides fast convergence. Experimental results show that the proposed algorithm significantly accelerates the convergence of X-ray CT image reconstruction with negligible overhead and can reduce OS artifacts when using many subsets.
Optimized linear combinations of channels for complex multiple-coil B1 field estimation with Bloch-Siegert B1 mapping in MRI

Bloch-Siegert B1 mapping for multiple-channel parallel excitation systems usually produces noisy estimates in low intensity regions. Methods that use linear combinations of multiple coils have been proposed to mitigate this problem. However, little work has been done to optimize these coil combinations to improve the signal-to-noise ratio of B1 mapping in a robust way. In this paper, we propose a Cramer-Rao Lower Bound analysis based method to optimize the coil combination matrix by minimizing the variance of B1 map estimation for the previously proposed Bloch-Siegert B1 mapping method. We illustrate how optimizing the coil combinations yields improved B1 estimates in a simulation of brain imaging with a 3T MRI scan.
Cramer-Rao lower bounds for biased image reconstruction

Since image reconstruction and restoration are ill-posed problems, unbiased estimators often have unacceptably high variance. To reduce the variance, one introduces constraints and smoothness penalties, which yields biased estimators. This bias precludes the use of the classical Cramer-Rao (CR) lower bound for the variance of an unbiased estimator. This paper presents a uniform bound for minimum variance subject to a bias gradient constraint. Since the bound is independent of any estimator, one can explore the fundamental tradeoff between bias and variance in ill-posed problems. We apply the bound to a linear Gaussian model, and demonstrate the optimality of a simple penalized least-squares estimator.<<ETX>>
Experimental evaluation for joint estimation approach

Single photon emission computed tomography (SPECT) provides a potential to perform in vivo quantification of the radioactivity and dose distributions in the process of evaluating radiopharmaceuticals. The inherent modest resolution in SPECT impedes the potential of accurate quantification. Previously, the authors investigated a joint estimation approach for combining SPECT functional information with high resolution, structurally correlated MRI anatomical information to improve the accuracy of SPECT quantification, and the computer simulation results showed that this approach can exploit MRI region information that matches the SPECT functional information and to reduce artifacts caused by mismatched MRI anatomical information. Here, the authors further describe the experimental evaluation of the joint estimation approach using actual SPECT and MRI imaging with an animal-sized phantom. They describe practical details in applying the joint estimation approach and present the experimental evaluation results of quantitative analysis.
Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

The sparsity of signals in a transform domain or dictionary has been exploited in applications, such as compression, denoising, and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically nonconvex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speed-ups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.
List mode EM reconstruction of Compton scatter camera images in 3-D

A method has been developed for List Mode EM reconstruction of Compton scattering camera images in 3D, using a previously reported 2-D technique and refining and adapting it to three dimensions. Spatial variation in the system sensitivity is determined by an approximate numerical integration which accounts for solid angle effects, absorption and escape probabilities, and variation in the differential angular scattering cross section. The method for computing the system transition probabilities uses a similar method to determine values in pixels along exact back-projected cones for each detected event, and uses pre-computed values of the inherent system resolution (which includes the effects of spatial and energy measurement resolution and Doppler broadening) to model the response in pixels neighboring the back-projected cone. The algorithm has been parallelized, permitting reconstruction of images using larger number of detected events in relatively constant time by adding additional processors. Results are presented using 3-D simulated data.
Gradient based image registration using importance sampling

Analytical gradient based non-rigid image registration methods, using intensity based similarity measures (e.g. mutual information), have proven to be capable of accurately handling many types of deformations. While their versatility is largely in part to their high degrees of freedom, the computation of the gradient of the similarity measure with respect to the many warp parameters becomes very time consuming. Recently, a simple stochastic approximation method using a small random subset of image pixels to approximate this gradient has been shown to be effective. We propose to use importance sampling to improve the accuracy and reduce the variance of this approximation by preferentially selecting pixels near image edges. Initial empirical results show that a combination of stochastic approximation methods and importance sampling greatly improves the rate of convergence of the registration process while preserving accuracy
Hardware acceleration of iterative image reconstruction for X-ray computed tomography

X-ray computed tomography (CT) images could be improved using iterative image reconstruction if the 3D cone-beam forward- and back-projection computations can be accelerated significantly. We investigated the feasibility of a field-programmable gate array (FPGA) implementation of the separable footprint (SF) forward projector. A 16-bit fixed-point quantization introduces negligible numerical errors without affecting the perceptual image quality. The SF-based 3D cone-beam projector can be efficiently parallelized and its memory bandwidth reduced by exploiting projection geometry and data locality. We demonstrate a fully pipelined, 75-way parallel hardware architecture of the SF forward projector on a Xilinx Virtex-5 FPGA that can complete one forward projection of a 320×320×61 object over 3,625 views in 6.3 seconds.
Accelerated Edge-Preserving Image Restoration Without Boundary Artifacts

To reduce blur in noisy images, regularized image restoration methods have been proposed that use nonquadratic regularizers (like l1 regularization or total-variation) that suppress noise while preserving edges in the image. Most of these methods assume a circulant blur (periodic convolution with a blurring kernel) that can lead to wraparound artifacts along the boundaries of the image due to the implied periodicity of the circulant model. Using a noncirculant model could prevent these artifacts at the cost of increased computational complexity. In this paper, we propose to use a circulant blur model combined with a masking operator that prevents wraparound artifacts. The resulting model is noncirculant, so we propose an efficient algorithm using variable splitting and augmented Lagrangian (AL) strategies. Our variable splitting scheme, when combined with the AL framework and alternating minimization, leads to simple linear systems that can be solved noniteratively using fast Fourier transforms (FFTs), eliminating the need for more expensive conjugate gradient-type solvers. The proposed method can also efficiently tackle a variety of convex regularizers, including edge-preserving (e.g., total-variation) and sparsity promoting (e.g., l1-norm) regularizers. Simulation results show fast convergence of the proposed method, along with improved image quality at the boundaries where the circulant model is inaccurate.
Fast variance computation for quadratically penalized iterative reconstruction of 3D axial CT images

Finding the variance of iteratively-reconstructed 3D axial CT images is useful for statistical analysis of these images or could be useful for dynamic, on-line beam intensity adjustment. Previous methods for finding the variance are either computationally intractable or approximations that take minutes per voxel to compute. In this paper, we propose a method that can generate a variance image for an entire volume in seconds by making approximations specific to third-generation 3D axial CT geometries. We compare the computation time and error of the resulting approximate image to the empirical image formed from many simulated realizations of a reconstruction.
NMR object boundaries: B-spline modeling and estimator performance

We give estimation error bounds and specify optimal estimators for continuous, closed boundary curves in an NMR image. The boundary is parameterized using periodic B-splines. A Cramer-Rao lower bound on mean-square-estimate error in the presence of system smoothing and Gaussian noise is derived, and the performance of maximum likelihood and penalized maximum likelihood estimators is compared to this bound. Finally, we comment on the usefulness of estimates of the boundary for providing anatomical side information in the reconstruction of functional tomographic images like those of a PET or SPECT system.
Sufficient condition for local invertibility of spatio-temporal 4D B-spline deformations

Recent advances in medical imaging technologies have made 4D image sequences available in clinical routine. As a consequence, image registration techniques are evolving from alignment of pairs of static volumetric images to spatio-temporal registration of dynamic (4D) images. Since the elastic image registration problem is ill-posed, additional prior information or constraints are usually required to regularize the problem. This work proposes to enforce local invertibility (diffeomorphism) of 4D deformations. A novel sufficient condition for local invertibility over continuous space and time is proposed and a practical regularization prior is designed from the theory. The method has been applied to an image registration (motion tracking) of a dynamic 4D CT image sequence. Results show that using proposed regularizer leads to deformations that are more plausible for respiratory motion than the standard approach without additional temporal regularization.
Determining total I-131 activity within a VoI using SPECT, a UHE collimator, OSEM, and a constant conversion factor

Accurate determination of activity within a volume of interest is needed during radiopharmaceutical therapies. Single-photon emission computed tomography(SPECT) is employed but requires a method to convert counts to activity. We use a phantom-based conversion; that is, we image an elliptical cylinder containing a sphere that has a known amount of 131-I activity inside. The regularized space alternating generalized expectation (SAGE) algorithm employing a strip-integral detector-response model was employed for reconstruction in previous patient evaluations. With that algorithm and a high-energy collimator, the estimates for sphere activity varied with changes in: 1) the level of uniform background activity in the cylinder; 2) the image resolution due to different values of the radius of rotation R; and 3) the volume of the sphere. When one used those to convert reconstructed counts within a patient tumor into an activity estimate, the resultant value may have been in error because of patient-phantom mismatch. As a potential remedy, in this paper, we use an ordered subsets expectation maximization (OSEM) algorithm with a 3-D depth-dependent detector-response model and an ultra-high-energy collimator. Results after 100 OSEM iterations and using a maximum counts registration show the estimates for sphere activity: 1) have a dependence on the level of background activity with a slope whose absolute magnitude is typically only 0.37 times that with SAGE; 2) are independent of R; and 3) are independent of sphere volume down to and including a sphere volume of 20 cm/sup 3/. We conclude that using a global-average conversion factor to relate counts to activity and no volume-based correction might be reasonable with OSEM. For a test of that conclusion, target activity is estimated for an anthropomorphic phantom containing a 100 cm/sup 3/ spherical tumor centrally located inferior to the lungs. With OSEM-based quantification, using: 1) a global-average conversion factor and 2) no volume-based correction, mean bias in the simulated-tumor activity estimate over 20 realizations is -7.37% (relative standard deviation =5.93%). With SAGE-based quantification using: 1) the conversion factor corresponding to the experimental estimate of background and 2) volume-based correction, the mean bias is -10.7% (relative standard deviation =2.37%). The mean bias is smaller in a statistically significant way and relative standard deviation is not more than a factor of 2.5 bigger with OSEM compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE.
Respiratory motion estimation from slowly rotating X-ray projections

As radiotherapy has become increasingly conformal, geometric uncertainties caused by breathing and organ motion have become an important issue. Accurate motion estimates may lead to improved treatment planning and dose calculation in radiation therapy. However, respiratory motion is difficult to study by conventional X-ray CT imaging since object motion causes inconsistent projection views leading to artifacts in reconstructed images. We propose to estimate the parameters of a nonrigid motion model from a set of projection views of the thorax that are acquired using a slowly rotating cone-beam CT scanner, such as a radiotherapy simulator. We use a conventionally reconstructed 3D thorax image, acquired by breath-hold CT, as a reference volume. We represent respiratory motion using a flexible parametric nonrigid motion model based on B-splines. The motion parameters are estimated by optimizing a regularized cost function that includes the squared error between the measured projection views and the reprojections of the deformed reference image. Preliminary 2D simulation results show that there is good agreement between the estimated motion and the true motion.
Forward-Projection Architecture for Fast Iterative Image Reconstruction in X-Ray CT

Iterative image reconstruction can dramatically improve the image quality in X-ray computed tomography (CT), but the computation involves iterative steps of 3D forward- and back-projection, which impedes routine clinical use. To accelerate forward-projection, we analyze the CT geometry to identify the intrinsic parallelism and data access sequence for a highly parallel hardware architecture. To improve the efficiency of this architecture, we propose a water-filling buffer to remove pipeline stalls, and an out-of-order sectored processing to reduce the off-chip memory access by up to three orders of magnitude. We make a floating-point to fixed-point conversion based on numerical simulations and demonstrate comparable image quality at a much lower implementation cost. As a proof of concept, a 5-stage fully pipelined, 55-way parallel separable-footprint forward-projector is prototyped on a Xilinx Virtex-5 FPGA for a throughput of 925.8 million voxel projections/s at 200 MHz clock frequency, 4.6 times higher than an optimized 16-threaded program running on an 8-core 2.8-GHz CPU. A similar architecture can be applied to back-projection for a complete iterative image reconstruction system. The proposed algorithm and architecture can also be applied to hardware platforms such as graphics processing unit and digital signal processor to achieve significant accelerations.
Scan time optimization for post-injection PET scans

Previous methods for optimizing the scan times for PET transmission and emission scans under a total scan time constraint were based on linear non-statistical methods and used noise equivalent counts (NEC) criteria. The scan times determined by NEC analysis may be suboptimal when nonlinear statistical image reconstruction methods are used. For statistical image reconstruction, the predicted variance in selected regions of interest is an appropriate alternative to NEC analysis. The authors propose a new method for optimizing the relative scan times (fractions) based on analytical approximations to the covariance of images reconstructed by both conventional and penalized-likelihood methods. The authors perform simulations to compare predicted standard deviations with empirical ones. Results show that for statistical transmission image reconstruction, the optimal fraction of the scan time devoted to transmission scanning is shorter than for conventional transmission smoothing.
ITERATIVE SORTING FOR 4DCT IMAGES BASED ON INTERNAL ANATOMY MOTION

Geometric uncertainties caused by respiratory motion complicate radiotherapy treatment planning. Therefore 4D CT imaging is important in characterizing anatomy motion during breathing. Current 4D CT imaging techniques using multislice CT scanners involve multiple scans at several axial positions and retrospective sorting processes. Most sorting methods are based on externally monitored signals recorded by external monitoring instruments, which may not always accurately catch the actual breathing status and may lead to severe discontinuity artifacts in the sorted CT volumes. We propose a method to reconstruct time-resolved CT volumes based on internal motion to avoid the inaccuracies caused by external breathing signals. In our method, we iteratively sort the 4D CT slices using internal motion based breathing indices. In each iteration, respiratory motion is estimated by updating a motion model to best match a deformed reference volume to each moving multi-slice sub-volumes. The breathing indices as well as the reference volumes are refined for each iteration based on the currently estimated respiratory motion. An example is presented to illustrate the feasibility of our 4D CT sorting method without using any external motion monitoring systems.
Complete-data spaces and generalized EM algorithms

Expectation-maximization (EM) algorithms have been applied extensively for computing maximum-likelihood and penalized-likelihood parameter estimates in signal processing applications. Intrinsic to each EM algorithm is a complete-data space (CDS)-a hypothetical set of random variables that is related to the parameters more naturally than the measurements are. The authors describe two generalizations of the EM paradigm: (i) allowing the relationship between the CDS and the measured data to be nondeterministic, and (ii) using a sequence of alternating complete-data spaces. These generalizations are motivated in part by the influence of the CDS on the convergence rate, a relationship that is formalized through a data-processing inequality for Fisher information. These concepts are applied to the problem of estimating superimposed signals in Gaussian noise, and it is shown that the new space alternating generalized EM algorithm converges significantly faster than the ordinary EM algorithm.<<ETX>>
Regularized emission image reconstruction using imperfect side information

The authors report a preliminary investigation of a spatially variant penalized-likelihood method for tomographic image reconstruction based on a Gibbs penalty. The penalty weights are determined from structural side information, such as the locations of anatomical boundaries in high-resolution magnetic resonance images. Such side information will be imperfect in practice, and a simple simulation demonstrates the importance of accounting for the errors in boundary locations. The authors discuss methods for prescribing the penalty weights when the side information is noisy. Simulation results suggest that even imperfect side information is useful for guiding spatially variant regularization.<<ETX>>
Object-based 3-D reconstruction of arterial trees from magnetic resonance angiograms.

By exploiting a priori knowledge of arterial shape and smoothness, subpixel accuracy reconstructions are achieved from only four noisy projection images. The method incorporates a priori knowledge of the structure of branching arteries into a natural optimality criterion that encompasses the entire arterial tree. An efficient optimization algorithm for object estimation is presented, and its performance on simulated, phantom, and in vivo magnetic resonance angiograms is demonstrated. It is shown that accurate reconstruction of bifurcations is achievable with parametric models.