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A vast amount of geographic information exists in natural language texts, such as tweets and news. Extracting geographic information from texts is called Geoparsing, which includes two subtasks: toponym recognition and toponym disambiguation, i.e., to identify the geospatial representations of toponyms. This paper focuses on toponym disambiguation, which is usually approached by toponym resolution and entity linking. Recently, many novel approaches have been proposed, especially deep learning-based approaches, such as CamCoder, GENRE, and BLINK. In this paper, a spatial clustering-based voting approach that combines several individual approaches is proposed to improve SOTA performance in terms of robustness and generalizability. Experiments are conducted to compare a voting ensemble with 20 latest and commonly-used approaches based on 12 public datasets, including several highly ambiguous and challenging datasets (e.g., WikToR and CLDW). The datasets are of six types: tweets, historical documents, news, web pages, scientific articles, and Wikipedia articles, containing in total 98,300 places across the world. The results show that the voting ensemble performs the best on all the datasets, achieving an average Accuracy@161km of 0.86, proving the generalizability and robustness of the voting approach. Also, the voting ensemble drastically improves the performance of resolving fine-grained places, i.e., POIs, natural features, and traffic ways., Comment: 32 pages, 15 figures

A vast amount of location information exists in unstructured texts, such as social media posts, news stories, scientific articles, web pages, travel blogs, and historical archives. Geoparsing refers to the process of recognizing location references from texts and identifying their geospatial representations. While geoparsing can benefit many domains, a summary of the specific applications is still missing. Further, there lacks a comprehensive review and comparison of existing approaches for location reference recognition, which is the first and a core step of geoparsing. To fill these research gaps, this review first summarizes seven typical application domains of geoparsing: geographic information retrieval, disaster management, disease surveillance, traffic management, spatial humanities, tourism management, and crime management. We then review existing approaches for location reference recognition by categorizing these approaches into four groups based on their underlying functional principle: rule-based, gazetteer matching-based, statistical learning-based, and hybrid approaches. Next, we thoroughly evaluate the correctness and computational efficiency of the 27 most widely used approaches for location reference recognition based on 26 public datasets with different types of texts (e.g., social media posts and news stories) containing 39,736 location references across the world. Results from this thorough evaluation can help inform future methodological developments for location reference recognition, and can help guide the selection of proper approaches based on application needs., Comment: 35 pages, 11 figures

BACKGROUND AND PURPOSE: Cerebral aneurysm is one of the most common cerebrovascular diseases, and SAH caused by its rupture has a very high mortality and disability rate. Existing automatic segmentation methods based on DLMs with TOF-MRA modality could not segment edge voxels very well, so that our goal is to realize more accurate segmentation of cerebral aneurysms in 3D TOF-MRA with the help of DLMs. MATERIALS AND METHODS: In this research, we proposed an automatic segmentation framework of cerebral aneurysm in 3D TOF-MRA. The framework was composed of two segmentation networks ranging from coarse to fine. The coarse segmentation network, namely DeepMedic, completed the coarse segmentation of cerebral aneurysms, and the processed results were fed into the fine segmentation network, namely dual-channel SE_3D U-Net trained with weighted loss function, for fine segmentation. Images from ADAM2020 (n=113) were used for training and validation and images from another center (n=45) were used for testing. The segmentation metrics we used include DSC, HD, and VS. RESULTS: The trained cerebral aneurysm segmentation model achieved DSC of 0.75, HD of 1.52, and VS of 0.91 on validation cohort. On the totally independent test cohort, our method achieved the highest DSC of 0.12, the lowest HD of 11.61, and the highest VS of 0.16 in comparison with state-of-the-art segmentation networks. CONCLUSIONS: The coarse-to-fine framework, which composed of DeepMedic and dual-channel SE_3D U-Net can segment cerebral aneurysms in 3D TOF-MRA with a superior accuracy.

In this paper, we study the sharp oracle bounds for Slope and Lasso and generalize the results in Bellec et al. (2018) to allow the case that the parameter vector is not exactly sparse and obtain the optimal bounds for $\ell_q$ estimation errors with $1\leq q\leq \infty$ by using some extended Restricted Eigenvalue type conditions.

Over the past decades, many individual nonconvex methods have been proposed to achieve better sparse recovery performance in various scenarios. However, how to construct a valid nonconvex regularization function remains open in practice. In this paper, we fill in this gap by presenting a unified framework for constructing the nonconvex regularization based on the probability density function. Meanwhile, a new nonconvex sparse recovery method constructed via the Weibull distribution is studied.

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established for both constrained and unconstrained models. The practical algorithms via both the iteratively reweighted $\ell_1$ and the difference of convex functions algorithms are presented. Numerical experiments are conducted to illustrate the improvement provided by the proposed approach in various scenarios. Its practical application in magnetic resonance imaging (MRI) reconstruction is studied as well.

In this paper, we propose a method for block sparse signal recovery that minimizes the block $q$-ratio sparsity $\left(\lVert z\rVert_{2,1}/\lVert z\rVert_{2,q}\right)^{\frac{q}{q-1}}$ with $q\in[0,\infty]$. For the case of $1

In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the $q$-ratio sparsity. When $1 < q \leq \infty$, both the theoretical analysis based on $q$-ratio constrained minimal singular values (CMSV) and the practical algorithms via nonlinear fractional programming are presented. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approaches over the state-of-the-art sparse recovery methods., Comment: 21 pages, 11 figures

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few research work about how to estimate block sparsity of real-valued signals, while there is, to the best of our knowledge, no investigation that has been conducted for complex-valued signals. In this paper, we propose a new method to estimate the block sparsity of complex-valued signal. Its statistical properties are obtained and verified by simulations. In addition, we demonstrate the importance of accurately estimating the block sparsity in signal recovery through a sensitivity analysis.

In this paper we introduce the $q$-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed $\ell_2/\ell_q$ and the mixed $\ell_2/\ell_1$ norms of the reconstruction errors for stable and robust recovery using block Basis Pursuit (BBP), the block Dantzig selector (BDS) and the group lasso in terms of the $q$-ratio BCMSV are investigated. We establish a sufficient condition based on the $q$-ratio block sparsity for the exact recovery from the noise free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, the $q$-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the $q$-ratio BCMSV based error bounds are tighter than the block restricted isotropic constant based bounds., Comment: arXiv admin note: text overlap with arXiv:1801.06358

Sparse recovery aims to reconstruct an unknown spare or approximately sparse signal from significantly few noisy incoherent linear measurements. As a kind of computable incoherence measure of the measurement matrix, $q$-ratio constrained minimal singular values (CMSV) was proposed in Zhou and Yu \cite{zhou2018sparse} to derive the performance bounds for sparse recovery. In this paper, we study the geometrical property of the $q$-ratio CMSV, based on which we establish new sufficient conditions for signal recovery involving both sparsity defect and measurement error. The $\ell_1$-truncated set $q$-width of the measurement matrix is developed as the geometrical characterization of $q$-ratio CMSV. In addition, we show that the $q$-ratio CMSVs of a class of structured random matrices are bounded away from zero with high probability as long as the number of measurements is large enough, therefore satisfy those established sufficient conditions. Overall, our results generalize the results in Zhang and Cheng \cite{zc} from $q=2$ to any $q\in(1,\infty]$ and complement the arguments of $q$-ratio CMSV from a geometrical view.

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization problems involve either simplifying assumptions, relaxations or high computational expenses. We propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the presented optimization problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Experiments on synthetic data and real-world images show that the proposed AADMM algorithm provides superior performance and is computationally cheaper, compared to the recently developed iterative convex refinement (ICR) algorithm.

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of measurements is reasonably large. Comparing to the restricted isotropic constant based performance analysis, the arguments in this paper are much more concise and the obtained bounds are tighter. Numerical experiments are presented to illustrate our theoretical results.

The theory of compressive sensing (CS) asserts that an unknown signal $\mathbf{x} \in \mathbb{C}^N$ can be accurately recovered from $m$ measurements with $m\ll N$ provided that $\mathbf{x}$ is sparse. Most of the recovery algorithms need the sparsity $s=\lVert\mathbf{x}\rVert_0$ as an input. However, generally $s$ is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0

We study the recovery conditions of weighted $\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of $k$-sparse phaseless recovery via weighted $\ell_1$ minimization. Numerical experiments are conducted to illustrate our results.

We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from $\ell_2$-constrained CS to $\ell_p$-constrained case with $p\geq 1$ and complements the recovery analysis for robust CS with $\ell_p$ loss function.

Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. Theoretically, an unknown signal with block structure can be accurately recovered from a few number of under-determined linear measurements provided that it is sufficiently block sparse. From the practical point of view, a severe concern is that the block sparse level appears often unknown. In this paper, we introduce a soft measure of block sparsity $k_\alpha(\mathbf{x})=\left(\lVert\mathbf{x}\rVert_{2,\alpha}/\lVert\mathbf{x}\rVert_{2,1}\right)^{\frac{\alpha}{1-\alpha}}$ with $\alpha\in[0,\infty]$, and propose an estimation procedure by using multivariate centered isotropic symmetric $\alpha$-stable random projections. The limiting distribution of the estimator is established. Simulations are conducted to illustrate our theoretical results.