nils-herrmann/clean_scirepeval huggingface dataset:
A variable splitting based algorithm for fast multi-coil blind compressed sensing MRI reconstruction

Recent work on blind compressed sensing (BCS) has shown that exploiting sparsity in dictionaries that are learnt directly from the data at hand can outperform compressed sensing (CS) that uses fixed dictionaries. A challenge with BCS however is the large computational complexity during its optimization, which limits its practical use in several MRI applications. In this paper, we propose a novel optimization algorithm that utilize variable splitting strategies to significantly improve the convergence speed of the BCS optimization. The splitting allows us to efficiently decouple the sparse coefficient, and dictionary update steps from the data fidelity term, resulting in subproblems that take closed form analytical solutions, which otherwise require slower iterative conjugate gradient algorithms. Through experiments on multi coil parametric MRI data, we demonstrate the superior performance of BCS over conventional CS schemes, while achieving convergence speed up factors of over 10 fold over the previously proposed implementation of the BCS algorithm.
Joint recovery of under sampled signals on a manifold: Application to free breathing cardiac MRI

We introduce novel algorithms for the joint recovery of an ensemble of signals that live on a smooth manifold from their under sampled measurements. Unlike current methods that are designed to recover a single signal assuming perfect knowledge of the manifold model, the proposed algorithms exploit similarity between the signals without prior knowledge of the underlying manifold structure. Our first algorithm is a two-step scheme, where the Laplacian of the graph associated with the manifold is estimated from similar under sampled measurements made on the signals; this Laplacian is used to formulate the problem as a penalized optimization scheme, where smoothness of the signals on the manifold is chosen as the penalty. The second algorithm is an iterative scheme that alternates between computation of the Laplacian and the signals. Validation of the proposed algorithms using simulations and experimental MRI data demonstrate their utility in accelerating free breathing cardiac MRI.
Algebraic Decomposition of Fat and Water in MRI

The decomposition of magnetic resonance imaging (MRI) data to generate water and fat images has several applications in medical imaging, including fat suppression and quantification of visceral fat. We introduce a novel algorithm to overcome some of the problems associated with current analytical and iterative decomposition schemes. In contrast to traditional analytical schemes, our approach is general enough to accommodate any uniform echo-shift pattern, any number of metabolites and signal samples. In contrast to region-growing method that use a smooth field-map initialization to resolve the ambiguities with the IDEAL algorithm, we propose to use an explicit smoothness constraint on the final fieldmap estimate. Towards this end, we estimate the number of feasible solutions at all the voxels, prior to the evaluation of the roots. This approach enables the algorithm to evaluate all the feasible roots, thus avoiding the convergence to the wrong solution. The estimation procedure is based on a modification of the harmonic retrieval (HR) framework to account for the chemical shift dependence in the frequencies. In contrast to the standard linear HR framework, we obtain the frequency shift as the common root of a set of quadratic equations. On most of the pixels with multiple feasible solutions, the correct solution can be identified by a simple sorting of the solutions. We use a region-merging algorithm to resolve the remaining ambiguity and phase-wrapping. Experimental results indicate that the proposed algebraic scheme eliminates most of the difficulties with the current schemes, without compromising the noise performance. Moreover, the proposed algorithm is also computationally more efficient.
Novel structured low-rank algorithm to recover spatially smooth exponential image time series

We propose a structured low rank matrix completion algorithm to recover a time series of images consisting of linear combination of exponential parameters at every pixel, from undersampled Fourier measurements. The spatial smoothness of these parameters is exploited along with the exponential structure of the time series at every pixel, to derive an annihilation relation in the k − t domain. This annihilation relation translates into a structured low rank matrix formed from the k − t samples. We demonstrate the algorithm in the parameter mapping setting and show significant improvement over state of the art methods.
Deformation Corrected Compressed Sensing (DC-CS): A Novel Framework for Accelerated Dynamic MRI

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover contrast enhanced dynamic magnetic resonance images from undersampled measurements. We introduce a formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage-based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to reduce the risk of convergence to local minima. The decoupling enabled by the proposed scheme enables us to apply this scheme to contrast enhanced MRI applications. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we observe superior image quality of the proposed DC-CS scheme in comparison to the classical k-t FOCUSS with motion estimation/correction scheme, and demonstrate reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation uncorrected signal.
Efficient NUFFT algorithm for non-Cartesian MRI reconstruction

We recently introduced a family of optimized interpolators to approximate the non-uniform Fourier transform of a finitely supported function. Theoretical comparisons indicated a significant improvement in performance over conventional approximations. In this paper, we study the utility of this approximation in the inversion of non-Cartesian MRI data. Using numerical simulations, we show that the new interpolators can provide iterative non-Cartesian inversion algorithms with considerably reduced memory demands. This will enable us to implement the algorithms on memory limited systems such as GPU, leading to a further acceleration in the iterative inversion of large MRI datasets.
Optimal steerable filters for feature detection

We present a new approach for the design of optimal steerable 2-D templates for feature detection. As opposed to classical schemes where the optimal 1-D template is derived and extended to 2-D, we directly obtain the 2-D template. We choose the template from a class of steerable functions based on the analytic optimization of a Canny-like criterion. Our approach gives more orientation selective templates that have simple closed form expression. We illustrate the method with the design of operators for edge and ridge detection and demonstrate their performance improvement in practical applications.
Spatial spectral modeling for robust MRSI

We propose a novel spatial spectral model for the reconstruction of magnetic resonance spectroscopic imaging (MRSI) signal. We penalize the compartmentalized spatial total variation norm of the signal to exploit the spatial properties of the metabolite peaks. The spectral signal is modeled as a sparse linear combination of spikes and polynomials to capture the peaks and baseline induced by unsuppressed water and lipids. We also use the high-resolution map of the magnetic field distribution within the slice to model the image acquisition, thus correcting for intra-voxel line shape distortions. The spectral model enables the stable recovery of the signal even in challenging spatial regions, while the spatial model suppresses the spectral leakage from extra-cranial fat and inter-voxel crosstalk. We acquire the MRSI signal using EPSI, while the high-resolution 3-D MRI information is derived using Dixon scans. The reconstruction of phantom and in vivo MRSI data demonstrate a significant improvement in spectral quality and accuracy over classical MRSI schemes.
Correction of B0 inhomogeneity distortion in magnetic resonance spectroscopic imaging

In this paper we reconstruct the 3-D MR spectroscopic data acquired using an echo-planar spectroscopic imaging (EPSI) sequence. We propose to compensate for B0 inhomogeneity artifact by using the B0 field map and T2* decay estimated from a higher resolution, multi-slice proton imaging data scanned with similar shimming to the EPSI one. We employ total variation (TV) regularization to obtain more uniform spectral peaks and lineshapes, and exploit the sparsity of the spectral data by using the ℓ1 norm in the reconstruction.
Iterative Shrinkage Algorithm for Patch-Smoothness Regularized Medical Image Recovery

We introduce a fast iterative shrinkage algorithm for patch-smoothness regularization of inverse problems in medical imaging. This approach is enabled by the reformulation of current non-local regularization schemes as an alternating algorithm to minimize a global criterion. The proposed algorithm alternates between evaluating the denoised inter-patch differences by shrinkage and computing an image that is consistent with the denoised inter-patch differences and measured data. We derive analytical shrinkage rules for several penalties that are relevant in non-local regularization. The redundancy in patch comparisons used to evaluate the shrinkage steps are exploited using convolution operations. The resulting algorithm is observed to be considerably faster than current alternating non-local algorithms. The proposed scheme is applicable to a large class of inverse problems including deblurring, denoising, and Fourier inversion. The comparisons of the proposed scheme with state-of-the-art regularization schemes in the context of recovering images from undersampled Fourier measurements demonstrate a considerable reduction in alias artifacts and preservation of edges.
A fast algorithm for structured low-rank matrix recovery with applications to undersampled MRI reconstruction

Structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. The main challenge in applying these schemes to large-scale problems is the dramatic increase in computational complexity and memory demand that results from a lifting of the image to a high-dimensional structured matrix. We introduce a fast and memory efficient algorithm that exploits the structure of the lifted matrix to work in the original non-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of MR images from undersampled measurements show that the resulting algorithm provides improved reconstructions over TV regularization with comparable computation time.
Subspace Aware Recovery of Low Rank and Jointly Sparse Signals

We consider the recovery of a matrix <inline-formula><tex-math notation="LaTeX">${\mathbf X}$</tex-math> </inline-formula>, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Each column of <inline-formula><tex-math notation="LaTeX">${\mathbf X}$</tex-math></inline-formula> is measured using a combination of two measurement matrices; one which is the same for every column, while the second measurement matrix varies from column to column. The recovery proceeds by first estimating the row subspace vectors from the measurements corresponding to the common matrix. The estimated row subspace vectors are then used to recover <inline-formula><tex-math notation="LaTeX">${\mathbf X}$</tex-math></inline-formula> from all the measurements using a convex program of joint sparsity minimization. Our main contribution is to provide sufficient conditions on the measurement matrices that guarantee the recovery of such a matrix using the above two-step algorithm. The results demonstrate quite significant savings in number of measurements when compared to the standard multiple measurement vector scheme, which assumes same time-invariant measurement pattern for all the time frames. We illustrate the impact of the sampling pattern on reconstruction quality using breath held cardiac cine MRI and cardiac perfusion MRI data, while the utility of the algorithm to accelerate the acquisition is demonstrated on MR parameter mapping.
Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods.
Optimized Least-Square Nonuniform Fast Fourier Transform

The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup tablebased evaluation of the interpolator; we use this metric to ensure that this component is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands.
Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the “HARDI reconstruction challenge” organized in the context of the “ISBI 2012” conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.
Blind compressed sensing with sparse dictionaries for accelerated dynamic MRI

Several algorithms that model the voxel time series as a sparse linear combination of basis functions in a fixed dictionary were introduced to recover dynamic MRI data from under sampled Fourier measurements. We have recently demonstrated that the joint estimation of dictionary basis and the sparse coefficients from the k-space data results in improved reconstructions. In this paper, we investigate the use of additional priors on the learned basis functions. Specifically, we assume the basis functions to be sparse in pre-specified transform or operator domains. Our experiments show that this constraint enables the suppression of noisy basis functions, thus further improving the quality of the reconstructions. We demonstrate the usefulness of the proposed method through various reconstruction examples.
Recovery of Low Rank and Jointly Sparse Matrices with Two Sampling Matrices

We provide a two-step approach to recover a jointly k-sparse matrix X, (at most k rows of X are nonzero), with rank r <; <; k from its under sampled measurements. Unlike the classical recovery algorithms that use the same measurement matrix for every column of X, the proposed algorithm comprises two stages, in each of which the measurement is taken by a different measurement matrix. The first stage uses a standard algorithm,  to recover any r columns (e.g. the first r) of X. The second uses a new set of measurements and the subspace estimate provided by these columns to recover the rest. We derive conditions on the second measurement matrix to guarantee perfect subspace aware recovery for two cases: First a worst-case setting that applies to all matrices. The second a generic case that works for almost all matrices. We demonstrate both theoretically and through simulations that when r <; <; k our approach needs far fewer measurements. It compares favorably with recent results using dense linear combinations, that do not use column-wise measurements.
Model based image reconstruction using deep learned priors (MODL)

We introduce a model-based image reconstruction framework, where we use a deep convolution neural network (CNN) based regularization prior. We rely on a recursive algorithm, which alternates between a CNN based denoising step and enforcement of data consistency. Unrolling the recursive algorithm yields a deep network that is trained using backpropagation. The unique aspect of this method is the use of the same CNN weights at each iteration, which makes the resulting structure consistent with the model-based formulation. Also, this approach reduces the number of trainable parameters, which hence lower the amount of training data needed. The use of a forward model also reduces the size of the network and enables the exploitation additional prior information available from calibration data. The use of the framework for multichannel MRI reconstruction provides improved reconstructions, compared to other state-of-the-art methods.
Structured low-rank recovery of piecewise constant signals with performance guarantees

We derive theoretical guarantees for the exact recovery of piecewise constant two-dimensional images from a minimal number of non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities of the image are localized to the zero level-set of a bandlimited function, which induces certain linear dependencies in Fourier domain, such that a multifold Toeplitz matrix built from the Fourier data is known to be low-rank. The recovery algorithm arranges the known Fourier samples into the structured matrix then attempts recovery of the missing Fourier data by minimizing the nuclear norm subject to structure and data constraints. This work adapts results by Chen and Chi on the recovery of isolated Diracs via nuclear norm minimization of a similar multifold Hankel structure. We show that exact recovery is possible with high probability when the bandlimited function describing the edge set satisfies an incoherency property. Finally, we demonstrate the algorithm on the recovery of undersampled MRI data.
Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.
A blind compressive sensing frame work for accelerated dynamic MRI

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic images from under-sampled measurements. This scheme models the the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. The dictionary and the sparse coefficients are simultaneously estimated from the under-sampled measurements. Since the number of degrees of freedom of this model is much smaller than that of current low-rank methods, this scheme is expected to provide improved reconstructions for datasets with considerable inter-frame motion. We develop an efficient majorize-minimize algorithm to solve for the dynamic images. We use a continuation strategy to minimize the convergence of the algorithm to local minima. Numerical comparisons of the BCS scheme with low-rank methods demonstrate the significant improvement in performance in the presence of motion.
A sparse reconstruction algorithm for parallel spiral MR spectroscopic imaging

In this paper we propose an efficient sparse reconstruction scheme for the parallel MRSI data acquired using a fast spiral scheme. We model the system using the MR priors estimated from the water reference scan. In our sparse reconstruction approach, we minimize the total variation and ℓ1 norm of the compartmentalized MRSI data in order to reduce noise, inhomogeneity distortions, and spectral leakage. We demonstrate significant improvement for in vivo brain results when compared to classical regularized SENSE MRSI reconstruction.