nils-herrmann/clean_scirepeval huggingface dataset:
Compartmentalized low-rank regularization with orthogonality constraints for high-resolution MRSI

We introduce a novel compartmental low rank algorithm for high resolution MR spectroscopic imaging. We model the field inhomogeneity compensated MRSI dataset as the sum of a lipid dataset and a metabolite dataset using the spatial compartmental information obtained from water reference data. Both these datasets are modeled as low-rank subspaces, and are assumed to be orthogonal to each other. We formulate the recovery of the dataset from spiral measurements as a low-rank recovery problem. Experiments using numerical phantom and in-vivo data demonstrates the ability of the algorithm to provide improved spatial resolution and nuisance signal free spectra.
MULTICHANNEL ESTIMATION OF COIL SENSITIVITIES IN PARALLEL MRI

We consider the problem of estimating receiver coil sensitivity functions in parallel MRI. By exploiting the multichannel nature of the problem, where multiple acquisitions of the same image function are obtained with different sensitivity weightings, we obtain a subspace-based framework for directly solving for the sensitivity functions. The proposed approach does not rely on the sum-of-squares assumption used in existing estimation schemes; this assumption tends to be violated towards the center of the image, thus leading to errors in the sensitivity estimates. Our approach eliminates this problem, producing superior sensitivity estimates in comparison to the sum-of-squares technique. In addition, the proposed restoration procedure is non-iterative, computationally efficient, and applicable both to cases where pilot scans are available or where auto-calibration data are collected with each scan. We present experimental results using actual and simulated data to assess the performance of our approach in comparison with existing methods
Low rank recovery with manifold smoothness prior: Theory and application to accelerated dynamic MRI

We introduce a regularized optimization algorithm to jointly recover signals that live on a low dimensional smooth manifold. The regularization penalty is the nuclear norm of the gradients of the signals on the manifold. We use this algorithm to reconstruct free breathing dynamic cardiac CINE MRI data. A novel acquisition scheme was used to facilitate the estimation of the manifold structure and recover high quality images. The results show that the method is an efficient alternative to traditional breath-held CINE exams.
Higher degree total variation for 3-D image recovery

We extend the novel higher degree total variation (HDTV) image regularization penalties to 3-D signals. These penalties generalize the popular total variation (TV) penalty to incorporate higher degree image derivatives. We adapt a fast alternating minimization algorithm designed for solving 2-D image recovery problems with HDTV regularization to the 3D setting. Numerical experiments on the compressed sensing recovery of 3-D magnetic resonance images show that HDTV and generalized HDTV improve the image quality significantly compared with TV. We also investigate the relationship between the recently introduced Hessian Schatten-norms and HDTV.
Three-dimensional feature detection using optimal steerable filters

We present a framework for feature detection in 3-D using steerable filters. These filters can be designed to optimally respond to a particular type of feature by maximizing several Canny-like criteria. The detection process involves the analytical computation of the orientation and corresponding response of the template. A post-processing step consisting of the suppression of non-maximal values followed by thresholding to eliminate insignificant features concludes the detection procedure. We illustrate the approach with the design of feature templates for the detection of surfaces and curves, and demonstrate their efficiency with practical applications.
Accelerated dynamic MRI using structured low rank matrix completion

We introduce a fast structured low-rank matrix completion algorithm with low memory & computational demand to recover the dynamic MRI data from undersampled measurements. The 3-D dataset is modeled as a piecewise smooth signal, whose discontinuities are localized to the zero sets of a bandlimited function. We show that a structured matrix corresponding to convolution with the Fourier coefficients of the signal derivatives is highly low-rank. This property enables us to recover the signal from undersampled measurements. The application of this scheme in dynamic MRI shows significant improvement over state of the art methods.
A Fast Majorize–Minimize Algorithm for the Recovery of Sparse and Low-Rank Matrices

We introduce a novel algorithm to recover sparse and low-rank matrices from noisy and undersampled measurements. We pose the reconstruction as an optimization problem, where we minimize a linear combination of data consistency error, nonconvex spectral penalty, and nonconvex sparsity penalty. We majorize the nondifferentiable spectral and sparsity penalties in the criterion by quadratic expressions to realize an iterative three-step alternating minimization scheme. Since each of these steps can be evaluated either analytically or using fast schemes, we obtain a computationally efficient algorithm. We demonstrate the utility of the algorithm in the context of dynamic magnetic resonance imaging (MRI) reconstruction from sub-Nyquist sampled measurements. The results show a significant improvement in signal-to-noise ratio and image quality compared with classical dynamic imaging algorithms. We expect the proposed scheme to be useful in a range of applications including video restoration and multidimensional MRI.
Accelerated dynamic MRI using self expressiveness prior

We introduce a self-expressiveness prior to exploit the redundancies between voxel profiles in dynamic MRI. Specifically, we express the temporal profile of each voxel in the dataset as a sparse linear combination of temporal profiles of other voxels. This scheme can be thought of as a direct approach to exploit the inter-voxel redundancies as opposed to low-rank and dictionary based schemes, which learn dictionaries from the data to represent the signal. The proposed representation may be interpreted as a union of subspaces model or as an analysis transform. The use of this algorithm is observed to considerably improve the recovery of myocardial perfusion MRI data from under sampled measurements.
Spark under 2-D fourier sampling

We consider the spark of submatrices of 2D-DFT matrices obtained by removing certain rows and relate it to the spark of associated 1D-DFT submatrices. A matrix has spark m if its smallest number of linearly dependent columns equals m. To recover an arbitrary fc-sparse vector, the spark of an observation matrix must exceed 2fc. We consider how to choose the rows of the 2D-DFT matrix so that it is full spark, i.e. its spark equals one more than its row dimension. We consider submatrices resulting from two sets of sampling patterns in frequency space: On a straight line and on a rectangular grid. We show that in the latter case full spark is rarely obtainable, though vectors with certain sparsity patterns can still be recovered. In the former case we provide a necessary and sufficient condition for full spark, and show that lines with integer slopes cannot attain it.
Neurite tracing in fluorescence microscopy images using ridge filtering and graph searching: principles and validation

To assist neurobiologists investigating the molecular mechanisms involved in neurite formation and differentiation, we have developed an interactive technique for the tracing and quantification of elongated image structures. The technique is based on an improved steerable filter for computing local ridge strength and orientation. It also uses a graph-searching algorithm with a novel cost function exploiting these image features to obtain globally optimal tracings between user-defined control points. To compare the performance of the technique to that of the currently used approach of fully manual delineation, four observers traced selected neurites in fluorescence microscopy images of cells in culture, using both methods. The results indicated that the proposed technique yields comparable accuracy in measuring neurite length, significantly improved accuracy in neurite centerline extraction, significantly improved reproducibility and reduced user interaction.
A fast majorize minimize algorithm for higher degree total variation regularization

The main focus of this paper is to introduce a computationally efficient algorithm for solving image recovery problems, regularized by the recently introduced higher degree total variation (HDTV) penalties. The anisotropic HDTV penalty is the fully separable L1 semi-norm of the directional image derivatives; the use of this penalty is seen to considerably improve image quality in biomedical inverse problems. We introduce a novel majorize minimize algorithm to solve the HDTV optimization problem, thus considerably speeding it over the previous implementation. Specifically, comparisons with previous iterative reweighted algorithm show an approximate ten fold speedup. The new algorithm enables us to obtain reconstructions that are free of patchy artifacts exhibited by classical TV schemes, while being comparable to state of the art total variation regularization schemes in run time.
3-D reconstruction of DNA filaments from stereo cryo-electron micrographs

We propose an algorithm for the 3-D reconstruction of DNA filaments from a pair of stereo cryo-electron micrographs. The underlying principle is to specify a 3-D model of a filament - described as a spline curve - and to fit it to the 2-D data using a snake-like algorithm. To drive the snake, we constructed a ridge-enhancing vector field for each of the images based on the maximum output of a bank of rotating matched filters. The magnitude of the field gives a confidence measure for the presence of a filament and the phase indicates its direction. We also propose a fast algorithm to perform the matched filtering. The snake algorithm starts with an initial curve (input by the user) and evolves it so that its projections on the viewing plane are in maximal agreement with the corresponding vector fields.
Real-time cardiac MRI using low-rank and sparsity penalties

We introduce a novel algorithm to reconstruct real-time cardiac MRI data from undersampled radial acquisitions. We exploit the fact that the spatio-temporal data can be represented as the linear combination of a few temporal basis functions. The current approaches that capitalize this property estimate the basis functions from central phase encodes, acquired with a fine temporal sampling rate. In contrast, we estimate the basis functions from the entire under-sampled data. By eliminating the need for training data, the proposed method can achieve potentially high acceleration factors. More importantly, the estimation of the temporal functions from the entire data significantly improves the quality of the basis functions, which inturn improves the quality of the reconstructions. Experiments on numerical phantoms show a significant reduction in artifacts at high acceleration factors, in comparison to current schemes.
Blind Compressive Sensing Dynamic MRI

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting l1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize-minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the l1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the l0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic magnetic resonance imaging applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes.
Sampling of periodic signals: a quantitative error analysis

We present an exact expression for the L/sub 2/ error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines, and bandlimited signal expansions. The formula takes the simple form of a Parseval's-like relation, where the Fourier coefficients of the signal are weighted against a frequency kernel that characterizes the approximation operator. We use this expression to analyze the behavior of the error as the sampling step approaches zero. We also experimentally verify the expression of the error in the context of the interpolation of closed curves.
Comprehensive reconstruction of multi-shot multi-channel diffusion data using mussels

Echo planar imaging (EPI)-based magnetic resonance imaging (MRI) data are often corrupted by Nyquist ghost artifacts resulting from odd-even shifts of the EPI read-outs. Algorithms that corrects for the Nyquist ghost artifacts rely on calibration scans that are collected prior to the data acquisition. However, a more complex pattern of ghosting artifacts arises when diffusion-weighted data are acquired using segmented k-space EPI read-outs. The additional under-sampling present in the segmented acquisitions and the inter-shot motion during diffusion weighted acquistion cause ghosting artifacts in addition to the EPI ghosting arising from odd-even shifts. We propose a comprehensive method that can remove the Nyquist-ghosting artifacts as well as the inter-shot motion-induced ghosting artifacts in diffusion weighted images in a single step from partial Fourier data without the need for a calibration scan. We show very high quality diffusion data recovery using the proposed method.
Recovery of Discontinuous Signals Using Group Sparse Higher Degree Total Variation

We introduce a family of novel regularization penalties to enable the recovery of discrete discontinuous piecewise polynomial signals from undersampled or degraded linear measurements. The penalties promote the group sparsity of the signal analyzed under a nth order derivative. We introduce an efficient alternating minimization algorithm to solve linear inverse problems regularized with the proposed penalties. Our experiments show that promoting group sparsity of derivatives enhances the compressed sensing recovery of discontinuous piecewise linear signals compared with an unstructured sparse prior. We also propose an extension to 2-D, which can be viewed as a group sparse version of higher degree total variation, and illustrate its effectiveness in denoising experiments.
Accelerating non-Cartesian sense for large coil arrays: Application to motion compensation in multishot DWI

Multi-shot sequences are often combined with techniques such as parallel imaging to achieve high fidelity images. For non-Cartesian sampling schemes, the reconstruction of such data becomes extremely computationally intensive. The problem of motion compensated SENSE reconstruction of non-Cartesian diffusion weighted images falls into a similar setting, when phase corrections are involved. Here we propose a new pipeline for the fast reconstruction of such data. The large array of composite sensitivity functions are replaced by a low-dimensional set of virtual sensitivity functions using a principal component analysis, thus enabling the evaluation of very few Fourier transforms. The time consuming gridding steps are replaced by a more efficient multiplication in the k-space, enabling further simplifications. Significant acceleration of reconstruction time is shown to be achieved with the new scheme. The algorithm in the general setting can accelerate SENSE reconstruction for large coil arrays.
Orthogonal quincunx wavelets with fractional orders

We present a new family of 2D orthogonal wavelets which use quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order /spl alpha/, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L/sub 2/(R/sup 2/) for any /spl alpha/>0. The wavelets are fractional in the sense that the approximation error at a given scale /spl alpha/ decays like O(a/sup /spl alpha//); they also essentially behave like fractional derivative operators. To make our construction practical, we propose an FFT-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.
Optimized non-uniform fast Fourier transform (NUFFT) for iterative tomographic reconstruction

The main focus of this paper is the efficient approximation of the non-uniform Fourier transform (NUFFT). We reformulate the standard NUFFT approximation as a projection of the exact discrete Fourier transform onto a shift-invariant space. This reformulation enables the use of sophisticated tools, developed in the context of shift-invariant representations, to analyze the performance of the approximation. Using these techniques, we derive the optimal scale factors for a specified interpolator. Assuming these scale factors, we develop a worst-case error criterion that is only dependent on the interpolating function. We propose an iterative re-weighted optimization algorithm to derive the optimized least square (OLS) interpolator. This interpolator significantly reduces the approximation error in comparison to the standard methods. The improved performance of this scheme, for low oversampling factors, could lead to a memory efficient algorithm for non-Cartesian Fourier inversion.
Coprime conditions for Fourier sampling for sparse recovery

This paper considers the spark of L × N submatrices of the N × N Discrete Fourier Transform (DFT) matrix. Here a matrix has spark m if every collection of its m - 1 columns are linearly independent. The motivation comes from such applications of compressed sensing as MRI and synthetic aperture radar, where device physics dictates the measurements to be Fourier samples of the signal. Consequently the observation matrix comprises certain rows of the DFT matrix. To recover an arbitrary k-sparse signal, the spark of the observation matrix must exceed 2k + 1. The technical question addressed in this paper is how to choose the rows of the DFT matrix so that its spark equals the maximum possible value L + 1. We expose certain coprimeness conditions that guarantee such a property.
Improved IDQC reconstruction for inhomogeneity corrected MR spectroscopy

In this paper, we focus on the reconstruction of iDQC MR spectroscopy data. Unlike standard 1-D MR spectroscopy schemes, iDQC acquires 2-D spectral data to decouple the magnetic field inhomogeneity effects from chemical shift information. This method suffers from a few limitations such as low intrinsic SNR, long acquisition time and the presence of a strong residual water peak. The standard IFFT based reconstruction schemes that rely on uniform sampling patterns have limited ability to overcome these problems. We propose a novel reconstruction scheme that employs a non-uniform sampling pattern, based on a flexible partitioning of the 2-D data-space. This approach enables the reconstruction of the metabolite region with a good resolution and signal to noise ratio, without being affected by aliases from the residual water signals. We pose the reconstruction problem as a conjugate gradient optimization. Using phantom data, we illustrate the significantly improved performance of the new method.
Unified reconstruction and motion estimation in cardiac perfusion MRI

We introduce a novel unifying approach to jointly estimate the motion and the dynamic images in first pass cardiac perfusion MR imaging. We formulate the recovery as an energy minimization scheme using a unified objective function that combines data consistency, spatial smoothness, motion and contrast dynamics penalties. We introduce a variable splitting strategy to simplify the objective function into multiple sub problems, which are solved using simple algorithms. These sub-problems are solved in an iterative manner using efficient continuation strategies. Preliminary validation using a numerical phantom and in-vivo perfusion data demonstrate the utility of the proposed scheme in recovering the perfusion images from considerably under-sampled data.
Accelerated first pass cardiac perfusion MRI using improved k − t SLR

Routinely trade-offs between the spatio-temporal resolution, volume coverage and SNR are done in first pass cardiac perfusion MRI due to the restricted imaging acquisition window (usually of the order of 300 to 400 msec per heart beat). In this paper, we demonstrate the use a low rank and sparse reconstruction scheme (k − t SLR) in obtaining highly accelerated first pass perfusion MR images and hence aim to reduce the above mentioned trade-offs. We introduce non-convex spectral norms and use a spatio-temporal total variation norm in recovering the dynamic signal matrix. We introduce an augmented Lagrangian optimization scheme in the context of matrix recovery to speed up the convergence of the algorithm. Extensive validations on in-vivo data are done to demonstrate the performance improvement of the proposed frame work.