nils-herrmann/clean_scirepeval huggingface dataset:
Efficient, Convergent SENSE MRI Reconstruction for Nonperiodic Boundary Conditions via Tridiagonal Solvers

Undersampling is an effective method for reducing scan acquisition time for MRI. Strategies for accelerated MRI, such as parallel MRI and compressed sensing MRI present challenging image reconstruction problems with nondifferentiable cost functions and computationally demanding operations. Variable splitting (VS) can simplify implementation of difficult image reconstruction problems, such as the combination of parallel MRI and compressed sensing, CS-SENSE-MRI. Combined with augmented Lagrangian (AL) and alternating minimization strategies, variable splitting can yield iterative minimization algorithms with simpler auxiliary variable updates. However, arbitrary variable splitting schemes are not guaranteed to converge. Many variable splitting strategies are combined with periodic boundary conditions. The resultant circulant Hessians enable  $\mathcal {O} (n \log {} n)$ computation but may compromise image accuracy at the spatial boundaries. We propose two methods for CS-SENSE-MRI that use regularization with nonperiodic boundary conditions to prevent wrap-around artifacts. Each algorithm computes one of the resulting variable updates efficiently in $\mathcal {O}\left(n\right)$ time using a parallelizable tridiagonal solver. AL-tridiag is a VS method designed to enable efficient computation for nonperiodic boundary conditions. Another proposed algorithm, ADMM-tridiag, uses a similar VS scheme but also ensures convergence to a minimizer of the proposed cost function using the alternating direction method of multipliers (ADMM). AL-tridiag and ADMM-tridiag show speeds competitive with previous VS CS-SENSE-MRI reconstruction algorithm AL-P2. We also apply the tridiagonal VS approach to a simple image inpainting problem.
A Bayesian Approach to Reconstruction from Incomplete Projections of a Multiple Object 3D Domain

An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data. Generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain. The object models, a statistical measurement model, and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem. For computational feasibility, a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion. The formulation and algorithm are restricted to objects whose center axis is a single-valued function of a fixed spatial coordinate. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector, at an average signal-to-noise ratio of 3.3.
Challenges and Open Problems in Signal Processing: Panel Discussion Summary from ICASSP 2017 [Panel and Forum]

This column summarizes the panel on open problems in signal processing, which took place on 5 March 2017 at the International Conference on Acoustics, Speech, and Signal Processing (ICASSP) in New Orleans, Louisiana. The goal of the panel was to draw attention to some of the challenges and open problems in various areas of signal processing and generate discussion on future research areas that can be of major significance and impact in signal processing. Five leading experts representing diverse areas within signal processing made up the panel.
Accelerated Regularized Estimation of MR Coil Sensitivities Using Augmented Lagrangian Methods

Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.
Evaluation of the ordered-subset transmission (OSTR) algorithm for transmission imaging on SPECT systems using axially overlapping cone-beams

Cone-beam transmission imaging employing medium-energy photons which penetrate parallel-hole collimators can be used to rapidly estimate attenuation maps for use in reconstruction of cardiac SPECT images. Such a transmission imaging geometry offers the advantage of eliminating the need to mechanically move the point-sources during imaging, and enables fast sequential transmission scans. The axial extent over which artifact-free attenuation maps can be reconstructed is limited by the cone-beam geometry and point-source collimation. We investigated irradiation of a single head by multiple point-sources whose asymmetric cone-beam fields overlap in the axial direction as a method of extending the axial coverage of the patient. This study reports on the development and testing of a penalized-likelihood algorithm for transmission reconstruction of overlapping asymmetric cone-beams. We evaluated this algorithm and optimized the reconstruction parameters through MCAT phantom simulations. We then and applied the algorithm to transmission measurements of an anthropomorphic phantom. The experimental work consisted of performing a series of flood and transmission measurements on the anthropomorphic phantom with shifted axial locations of point-sources. We summed the projection data from individual measurements to simulate the projection data for a multiple point-source system. With the proposed penalized-likelihood algorithm, the full axial extent (20.5 cm) of the anthropomorphic phantom was reconstructed for the overlapping cone-beam geometry with two point-sources per camera head.
Noise characteristics of the FORE+OSEM(DB) reconstruction method for the MiCES PET scanner

The FORE+OSEM(DB) image reconstruction method has been proposed for the fully-3D MiCES PET scanner under construction at the University of Washington. It is based on Fourier rebinning followed by 2D OSEM and an incorporated model of detector blurring (DB). As an extension, this paper presents the noise/resolution characteristics of this method. Multiple realizations were simulated to estimate the noise properties of the algorithm. The results are compared with OSEM followed by post reconstruction 3D Gaussian smoothing. The results show that the incorporation of detector blurring (OSEM(DB)) into the system matrix improves resolution compared to OSEM, while also inducing an increased variance at all radial locations. In addition, radially-varying noise characteristics are more apparent with OSEM(DB) than with OSEM.
Non-parametric tracking of shift and shape functions in medical images

Several important estimation problems, in particular the quantification of blood vessel position and radius from projections, involve tracking of dynamics shift band shape parameters. The authors present an alternative algorithm for tracking shift and shape parameters that is based on nonparametric cubic-spline smoothing. Rather than requiring a known Gauss-Markov model, the algorithm assumes only that the shift and shape functions be smoothly varying in a sense defined. They discuss the physical motivation for their (global) optimality criterion, derive an efficient algorithm for computing the optimal estimates, and demonstrate the performance on angiographic data. The performance of the algorithm is demonstrated on simulated angiogram data.<<ETX>>
Convolutional Dictionary Learning: Acceleration and Convergence

Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared with the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large data sets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.
Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography

Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For each estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usually resort to numerical simulations to examine properties of the mean and variance of each estimators. This paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters. We derive the approximations using the implicit function theorem, the Taylor expansion, and the chain rule. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. As illustrations, we demonstrate that the approximations work well in two tomographic imaging applications with Poisson statistics. We also describe a "plug-in" approximation that provides a remarkably accurate estimate of variability even from a single noisy Poisson sinogram measurement. The approximations should be useful hi a wide range of estimation problems.
Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography

Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators. This paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters. We derive the approximations using the implicit function theorem, the Taylor expansion, and the chain rule. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. As illustrations, we demonstrate that the approximations work well in two tomographic imaging applications with Poisson statistics. We also describe a "plug-in" approximation that provides a remarkably accurate estimate of variability even from a single noisy Poisson sinogram measurement. The approximations should be useful in a wide range of estimation problems.
Space-alternating generalized expectation-maximization algorithm

The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. The paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. The authors prove that the sequence of estimates monotonically increases the penalized-likelihood objective, derive asymptotic convergence rates, and provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, the SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.
Nonparametric fixed-interval smoothing with vector splines

A computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances is presented. This algorithm provides an alternative to the optimal smoothing algorithms that hinge on (possibly inaccurate) parametric state-space models. Automatic procedures that use the measurements to determine how much to smooth are developed and compared. This adaptation allows the data to speak for itself without imposing a Gauss-Markov model structure. A nonparametric approach to covariance estimation for the case of independently identically distributed (i.i.d.) measurement errors is presented. Monte Carlo simulations demonstrate the performance of the algorithm.
Penalized likelihood transmission image reconstruction:unconstrained monotonic algorithms

Statistical reconstruction algorithms in transmission tomography yield improved images relative to the conventional FBP method. The most popular iterative algorithms for this problem are the conjugate gradient (CG) method and ordered subsets (OS) methods. Neither method is ideal. OS methods "converge" quickly, but are suboptimal for problems with factored system matrices. Nonnegativity constraints are not imposed easily by the CG method. To speed convergence, we propose to abandon the nonnegativity constraints (letting the regularization discourage the negative values), and to use quadratic surrogates to choose the step size rather than using an expensive line search. To ensure monotonicity, we develop a modification of the transmission log-likelihood. The resulting algorithm is suitable for large-scale problems with factored system matrices such as X-ray CT image reconstruction with afterglow models. Preliminary results show that the regularization ensures minimal negative values, and that the algorithm is indeed monotone.
Preconditioning methods for shift-variant image reconstruction

Preconditioning methods can accelerate the convergence of gradient-based iterative methods for tomographic image reconstruction and image restoration. Circulant preconditioners have been used extensively for shift-invariant problems. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. For inverse problems that are approximately shift-invariant (i.e. approximately block-Toeplitz or block-circulant Hessians), circulant or Fourier-based preconditioners can provide remarkable acceleration. However, in applications with nonuniform noise variance (such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging), the Hessian of the (penalized) weighted least-squares objective function is quite shift-variant, and the Fourier preconditioner performs poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that more accurately approximate the Hessian matrices of shift-variant imaging problems. Compared to diagonal or Fourier preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. Applications to position emission tomography (PET) illustrate the method.
Low-Rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery fromundersampledmeasurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamicmagnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method.
Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.
Feasibility study of Compton scattering enchanced multiple pinhole imager for nuclear medicine

This paper presents a feasibility study of a Compton scattering enhanced (CSE) multiple pinhole imaging system for gamma rays with energy of 140keV or higher. This system consists of a multiple-pin hole collimator, a position sensitive scintillation detector as used in standard Gamma camera, and a Silicon pad detector array, inserted between the collimator and the scintillation detector. The problem of multiplexing, normally associated with multiple pinhole system, is reduced by using the extra information from the detected Compton scattering events. In order to compensate for the sensitivity loss, due to the low probability of detecting Compton scattered events, the proposed detector is designed to collect both Compton scattering and Non-Compton events. It has been shown that with properly selected pinhole spacing, the proposed detector design leads to an improved image quality.
Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE

Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate [based on the principle of Stein's unbiased risk estimate (SURE)] of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the l1-norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction.