Recovery error bounds of tail-minimization and the global convergence rate of an efficient proximal alternating algorithm for sparse signal recovery are investigated in this article. Tail-minimization aims to minimize the energy in the complement Tc of an estimated support T. Under the restricted isometry property (RIP) condition, we establish improved recovery error bounds for both the tail-ℓ1 minimization and the tail-lasso models. Notably, we demonstrate that the RIP condition can be significantly relaxed, allowing the RIP constant to approach 1 as the estimation T closely approximates the true support S. To efficiently solve the tail-lasso problem, we introduce a Hadamard product parametrization that renders the loss function differentiable. This formulation enables the use of a simple proximal alternating minimization algorithm with closed-form solution to find global minimizers. Leveraging landscape analysis and the Kurdyka-Łojasiewicz inequality, we establish the global convergence of the proposed algorithm. Numerical experiments validate that our algorithm substantially enhances signal recovery performance compared to state-of-the-art methods.

Analyses of a tail-l(2,2) minimization (tail-l(2,2)) approach for joint sparse recovery in the multiple measurement vectors (MMV) model are provided in this article. Unlike traditional l(2) minimization, the tail-l(2,2) technique has a remarkable sparse recovery capacity. Recovery guarantee analysis also reveals the rank enrichment effect from the number of measurements L with improved recovery rate. We show that the probability of successful recovery approaches 1 as the number of measurement vectors L increases and the cardinality of T (c) boolean AND S approaches 0, where T is an estimated support of the true solution index set S. Error bound analyses with tractable constants are also carried out without relying on the typical (tail-) null space property (NSP) and/or the restricted isometry property (RIP) because of the l(2) nature of the problem. These MMV theoretical results require nontrivial technique analyses from that of single measurement vector (SMV) cases. The efficiency of the tail-l(2,2) technique is particularly significant, as for each estimated T there are analytical tail-least square solutions. Numerical experiments validate the probabilistic results and demonstrate the superior effectiveness and efficiency of the tail-l(2,2) profile algorithm in sparse selections.

This article presents a systematic analysis for the generalized tail-atomic norm method in gridless spectrum estimations. The technique is to impose a tail-penalty on the complement of an estimated frequency set F. In gridless formulations, the complementary frequency set F-c equivalent to T\F is a continuous spectrum, where T is the frequency torus. Hence, to match the discrete measure of r frequencies in the measurement model, tail-penalty is preferably imposed over sufficiently "dense" samples of this continuum F-c. Such "density" requirement coincides with the beneficial sparsity enhancement to the amplitude variable. This naturally extends the original m x r (r < m) steering matrix to an over-complete m x n system, often with n >> m. A key contribution of this paper is the derivation of an equivalent semi-definite programming (SDP) solution for this generalized m x n-tail-atomic norm formulation. We further extend the analysis to the multiple measurement vector (MMV) model, showing its superior frequency recovery capabilities. Extensive numerical experiments are conducted, comparing the proposed framework with several state-of-the-art gridless techniques. The results demonstrate that the generalized tail-atomic norm method achieves significant improvements in both frequency estimation capacities and robustness against noise across a range of signal-to-noise ratios.

In order to solve the problems of low direction-finding accuracy, insufficient signal separation capability and limited resolution caused by unreasonable subarray allocation in spatial smoothing techniques for coherent sources, an improved Multi-Strategy Collaborative Simulated Annealing (MSC-SA) algorithm is proposed for subarray partition. The global optimization ability and computational efficiency of the algorithm are improved by preserving the initial solution and introducing steering vector condition number to guide the improvement of neighborhood structure. And the adaptation function based on spatial resolution is constructed for comprehensively consideration of the direction-finding accuracy and algorithm performance. Through three sets of simulation experiments, compared with the existing methods, the improved MAC-SA algorithm demonstrates faster convergence and superior performance in direction-finding accuracy, signal separability, and global optimization capability. The proposed algorithm effectively improves the accuracy and reliability of signal direction finding in complex electromagnetic environment.

We investigate the effectiveness and efficiency of the iterative tail-t2 2 minimization (tail-t2 2-min) technique for its sparse selection capabilities. We conduct profile analyses on the tail-t2 2-min, establishing the equivalence of the tail-t2 2-min problem to a two-stage profile t2 2 formulation, both featuring analytical solutions. The tail null space property (NSP) of sensing matrix A is shown to be equivalent to the NSP of the newly defined profile matrix A . Besides the error bound analysis for the tail-t2 2-min under the typical tail-NSP condition, a novel error bound of the tail-t2 2-min formulation is also established without relying on NSP or restricted isometry property (RIP) assumptions. It merely contains tractable coefficients of A , and offers insights into successful recovery, with the observation of the convergent iterative procedure. Numerical studies and the applications to image reconstruction demonstrate the superiority and fast convergence of the tail-t2 2 sparse solution over state-of-the-art sparse selection methodologies. The sparsity level of a signal that the tail-t2 2 profile algorithm guarantees the recovery is around 41% higher than that of the basis pursuit algorithm. The analytical solutions of the tail-t2 2 method at each iteration also ensure that the tail-t2 2 sparse recovery process is notably fast, especially for high dimensions and high sparsity levels.

Recovery error bounds of tail-minimization and the rate of convergence of an efficient proximal alternating algorithm for sparse signal recovery are considered in this article. Tail-minimization focuses on minimizing the energy in the complement T^c of an estimated support T. Under the restricted isometry property (RIP) condition, we prove that tail-ℓ_1 minimization can exactly recover sparse signals in the noiseless case for a given T. In the noisy case, two recovery results for the tail-ℓ_1 minimization and the tail-lasso models are established. Error bounds are improved over existing results. Additionally, we show that the RIP condition becomes surprisingly relaxed, allowing the RIP constant to approach 1 as the estimation T closely approximates the true support S. Finally, an efficient proximal alternating minimization algorithm is introduced for solving the tail-lasso problem using Hadamard product parametrization. The linear rate of convergence is established using the Kurdyka-Łojasiewicz inequality. Numerical results demonstrate that the proposed algorithm significantly improves signal recovery performance compared to state-of-the-art techniques.

We investigate the effectiveness and efficiency of the iterative tail-ℓ2 minimization (tail-ℓ2-min) technique for its sparse selection capabilities. We conduct profile analyses on the tail-ℓ2-min, establishing the equivalence of the tail-ℓ2-min problem to a two-stage profile ℓ2 formulation, both featuring analytical solutions. The tail null space property (NSP) of sensing matrix A is shown to be equivalent to the NSP of the newly defined profile matrix Ã. Besides the error bound analysis for the tail-ℓ2-min under the typical tail-NSP condition, a novel error bound of the tail-ℓ2-min formulation is also established without relying on NSP or restricted isometry property (RIP) assumptions. It merely contains tractable coefficients of A, and offers insights into successful recovery, with the observation of the convergent iterative procedure. Numerical studies and the applications to image reconstruction demonstrate the superiority and fast convergence of the tail-ℓ2 sparse solution over state-of-the-art sparse selection methodologies. The sparsity level of a signal that the tail-ℓ2 profile algorithm guarantees the recovery is around 41% higher than that of the basis pursuit algorithm. The analytical solutions of the tail-ℓ2 method at each iteration also ensure that the tail-ℓ2 sparse recovery process is notably fast, especially for high dimensions and high sparsity levels.

Recovery guarantee analyses of sparse signals by the tail- & ell;(2) minimization approach are presented. Known for the lack of sparse recovery capacity by traditional & ell;(2) minimization, its variation by an iterative tail- & ell;(2) penalty procedure, however, is shown to be exceedingly effective in sparse selections. The analytical close-form solutions of the tail- & ell;(2) formulation also reveal its superb efficiency. This article is focused on the analyses of the successful recovery by the tail- & ell;(2) technique. A necessary and sufficient condition for the uniqueness of the tail- & ell;(2) minimizer is established, which is seen inherently different from that of a similar tail- & ell;(1) minimization problem. The inherent differences lead to further analyses of sufficient conditions for the uniqueness, and a notion of admissible solutions. Successful probability analysis is then carried out based on these conditions. The estimated probability of successful recovery P-T is righteously related to the cardinality of T-c boolean AND S , where T is an estimated support of the solution index S . The smaller the divided by T-c boolean AND S divided by is, the greater the PT will be, and PT naturally approaches 1 as divided by T-c boolean AND S divided by approaches 0. Numerical experiments sufficiently validate the efficiency and the successful probability of the sparse signal recovery by the tail- & ell;(2) minimization procedure.

An effective tail-atomic norm methodology and algorithms for gridless spectral estimations are developed with a tail-minimization mechanism. We prove that the tail-atomic norm can be equivalently reformulated as a positive semi-definite programming (PSD) problem as well. Some delicate and critical weighting constraints are derived. Iterative tail-minimization algorithms based on PSD programming are also derived and implemented. Extensive simulation results demonstrate that the tail-atomic norm mechanism substantially outperforms state-of-the-art gridless spectral estimation techniques. Numerical studies also show that the tail-atomic norm approach is more robust to noisy measurements than other known related atomic norm methodologies.

A tail-Hadamard product parametrization (tail-HPP) approach is proposed for sparse signal recovery in compressed sensing. The algorithm has both the efficiency of the HPP technique and the much greater capacity of signal recovery enabled by the tail- t 1 -minimization approach. We prove that the tail-HPP approach is equivalent to the tail- t 1 -minimization problem. The efficiency of the tail-HPP algorithm is clearly evident compared to direct solution approaches of the tail- t 1 -minimization problem. These superiority of the tail-HPP algorithm is confirmed by extensive simulation experiments in comparison with state-of-the-art sparse recovery techniques.

This study proposes a novel solution using sensors with limited sensing range to estimate the random appearance or disappearance of multi-object trajectories with unknown object detection profiles under nonuniform clutter background. Specifically, assuming that no objects occur within the sensors' observable area, the unknown clutter intensity involving the average false alarms per scan and nonuniform clutter density is first estimated by adopting the joint combination of maximum likelihood (ML) and model-based clustering methods. Then, the unknown object detection profile can be calculated by marginalizing the fluctuating signal-to-noise ratio (SNR) in a random manner. Further, the TPMB filter is utilized to estimate trajectories from the first principle, after which the estimated parameters of clutter intensity and the detection probability are fed to the TPMB filtering, thereby improving the performance on completeness and robustness of estimation trajectories. Simulation and experimental results demonstrated that our proposed solution exhibits excellent tracking accuracy compared with state-of-the-art solutions involving robust MS generalized LMB (R-MS-GLMB) and dynamic parameter GLMB (DP-GLMB) filters.

Inspired by the fast iterative shrinkage-thresholding algorithm (FISTA), a tail-FISTA method based on the tail-ℓ1 minimization is proposed and analyzed for sparse signal recoveries. Solutions using the profile and the direct methods are both derived. It is also shown that the tail-FISTA method has the convergence rate of O(1/n2) for a given support index T. The tail-FISTA is therefore a much more efficient technique solving the tail-ℓ1 minimization problem than the usual basis pursuit solutions. The superior performance is also demonstrated through extensive numerical simulations in comparison with state-of-the-art algorithms. As an example, for A∈R64×128, traditional algorithms may recovery signals up to sparsity s≤15, while the tail-FISTA can recovery signals with sparsity s≤25. An image restoration/deblurring application is also studied among other techniques to demonstrate the effectiveness of the tail-FISTA technique.

Recovery guarantee analyses of the tail- $ \ell _{2,1}$ minimization approach applied to multiple measurement vector (MMV) model are presented. Exact joint sparse recovery from the MMV model benefits from the rank enrichment of $rank(\boldsymbol{X})$ . Generally speaking, unique sparse solution exists for sparsity level $k < K_{0} \equiv [rank(\boldsymbol{X})+spark(\boldsymbol{A})-1]/2$ . We observe in extensive empirical tests that the MMV tail- $ \ell _{2,1}$ minimization approach is capable of recovering signals of the sparsity level up to $spark(\boldsymbol{A})$ , even for $ rank(\boldsymbol{X})\ll k$ , significantly beyond the rank-enriched upper bound $ K_{0}$ . This phenomenon is now known to be the measure theoretical uniqueness solution of the MMV problem. To analyze the greater recovery capacity of the MMV tail- $ \ell _{2,1}$ minimization approach, two necessary and sufficient conditions for the unique solution are established. It is shown that these two tail- $ \ell _{2,1}$ solution conditions are more likely to hold than comparable conditions of the conventional $ \ell _{2,1}$ minimization approach. Furthermore, theoretical recovery guarantee analyses of the tail-minimization approach are carried out. Specifically, two recovery probability estimates are derived. These successful recovery probabilities are shown to approach 1 not only as the number of measurements $L$ increases (exponentially) but also as $|T^{c} \cap S|\to 0$ , where $T$ is an estimation of the support index set $S$ . That the MMV tail- $ \ell _{2,1}$ minimization algorithm can recover signals of sparsity level beyond $ K_{0}$ and approaching $ spark(\boldsymbol{A})$ is sufficiently illustrated from these recovery probabilities.

Inspired by the iteratively reweighted least squares (IRLS) algorithm with 1 ≤ q ≤ 2, a tail-IRLS algorithm is proposed to solve the ℓ q (1 ≤q≤ 2) minimization problem. Detailed derivation of the tail-IRLS algorithm is provided. Reweighted least square method enables ℓ q (1 ≤q≤ 2) minimization to possess some limited sparse selection capabilities. Tail-IRLS greatly enhances the sparse recovery capacity. One significant characteristic is that there is analytical solution at each iteration. Numerical simulations show the tail-IRLS algorithm is far superior to IRLS algorithm and many state-of-the-art algorithms.

针对瓦斯监控预警系统中的传感器节点能量有限及传输带宽有限,为减少信息传输量和布置节点的数据量,采用基于零空间调整的重构方法对瓦斯数据进行重构.瓦斯传感器对应的观测矩阵是瓦斯传感器的脉冲响应函数循环而构成的循环矩阵,应用高斯函数序列构造的循环矩阵来模拟.选用不同煤矿的多组瓦斯监测数据作为实验数据,对瓦斯数据进行快速傅里叶变换,观测矩阵分别使用循环矩阵和随机矩阵.重构实验结果表明,模拟脉冲响应函数的循环矩阵对瓦斯检测信号重构效果较好,当采样率一定范围减少时,循环矩阵下重构的平均误差约5％.因此,实际工程中可由降低50％采样率的数据来重构原始数据,显著减少数据采样点数,节省工程检测成本.一定范围内可用低分辨率的瓦斯传感器代替高分辨率的瓦斯传感器,以降低构建瓦斯监控物联网的成本.

Iterative algorithms based on thresholding, feedback, and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and efficient, particularly for large-scale problems. The core algorithm is shown to converge in finitely many steps under a (preconditioned) restricted isometry condition. We derive in this article the number of iterations to guarantee the convergence of the NST+HT+FB algorithm. Moreover, an accelerated class of adaptive feedback scheme of the iterative algorithm, termed NST+HT+f -FB, is proposed and analyzed. The scheme NST+HT+f -FB has a variable/adaptive index selection and different feedback principles at each iteration defined by a function f(k). It is even more effective, both from its ability to recover sparse signals with a larger number of non-zeros and from its rate of convergence. The convergence of the accelerated scheme is established. The finite number of iterations for guaranteed convergence by the NST+HT+f -FB scheme is also obtained. Furthermore, it is possible to accelerate the rate of convergence and improve the condition of convergence by selecting an appropriate size of the thresholding index set Tk per iteration. The theoretical findings are validated through extensive numerical experiments. It has been shown that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art greedy algorithms. Detailed comparisons are provided.

The tail-minimization approach is applied to the joint sparse multiple measurement vector (MMV) model and direction of arrival (DOA) estimations. The mechanism is to estimate the support T of the jointly sparse matrix and minimize the energy in the complement T-C of T during each iteration. An MMV tail null-space property (MMV-tail-NSP) is derived, which is shown to be necessary and sufficient for the unique solution of the MMV tail minimization problem. The MMV-tail-NSP condition is also shown to be more likely to hold than that of the conventional MMV-NSP for any given MMV basis pursuit problem. Two recovery guarantees and error bound analyses are also derived based on the MMV-robusttail-NSP condition and merely the MMV-tail-NSP assumption, respectively. Study shows that the MMV tail-minimization approach is among the most effective techniques for the MMV DOA model. In particular, the MMV tail-minimization approach is able to recover signals of rank-enriched sparsity level K-0 = [spark(A) - 1+ rank(X)]/2 . In fact, this approach can handle signal recovery of greater sparsity levels than that by others. The advantages of the MMV tail-minimization approach are also reflected in numerous aspects such as handling low signal-to-noise ratio (SNR), limited number of snapshots, and correlated source signals. Results are more accurate with higher resolution as well. It is also capable of detecting the number of sources and estimating DOAs simultaneously. All these characteristics and advantages are fully evidenced by extensive simulation studies. (C) 2021 Published by Elsevier B.V.

We propose tail fast iterative shrinkage-thresholding algorithm (tail-FISTA) to solve compressed sensing problem, and it considers fast iterative shrinkage-thresholding algorithm (FISTA) method to solve tail- ℓ 1 minimization problem. By means of the profile method, the tail- ℓ 1 minimization problem is rewritten as a transformed ordinary ℓ 1 minimization problem, and its solution can be obtained by FISTA. FISTA is attractive due to the computational simplicity and well global rate of convergence rate O(1/n 2 ). In simulation study, the performance of numerical examples is better than traditional compressed sensing algorithms. From the application of tail-FISTA, we can find that tail-FISTA is a potential compressed sensing algorithm.

Since magnetic resonance imaging (MRI) has superior soft tissue contrast, contouring (brain) tumor accurately by MRI images is essential in medical image processing. Segmenting tumor accurately is immensely challenging, since tumor and normal tissues are often inextricably intertwined in the brain. It is also extremely time consuming manually. Late deep learning techniques start to show reasonable success in brain tumor segmentation automatically. The purpose of this study is to develop a new region-ofinterest-aided (ROI-aided) deep learning technique for automatic brain tumor MRI segmentation. The method consists of two major steps. Step one is to use a 2D network with U-Net architecture to localize the tumor ROI, which is to reduce the impact of normal tissue’s disturbance. Then a 3D U-Net is performed in step 2 for tumor segmentation within identified ROI. The proposed method is validated on MICCAI BraTS 2015 Challenge with 220 high Gliomas grade (HGG) and 54 low Gliomas grade (LGG) patients’ data. The Dice similarity coefficient and the Hausdorff distance between the manual tumor contour and that segmented by the proposed method are 0.876 ±0.068 and 3.594±1.347 mm, respectively. These numbers are indications that our proposed method is an effective ROI-aided deep learning strategy for brain MRI tumor segmentation, and a valid and useful tool in medical image processing.

In practical radar detection applications, due to the limitation of the beam width of the pattern, limited field of view (FOV) lacks the overall perception ability of the area of interest (AOI). Especially, when unknown and time-varying targets appear in AOI, it can easily lead to missing even wrong tracking of key objects. In view of the above problems, the radar network is adopted to fuse the observation data of limited multi-view to obtain the global field of view information, and then realize the trajectories estimation of multi-object in the fusion center. Based on FInite Set STatistics (FISST) framework, mapping the newborn and death process of multiple targets within FOVs as multi-Bernoulli process, the posteriori density of multi-objects is propagated recursively followed Bayesian criterion in time. The simulation results of multi-object trajectories estimation with four kinds of multi-Bernoulli (MB) filters are given under three scenarios, which illustrates that the number of interest objects and the accuracy of trajectories estimation are improved, along with the increase of the number of local observation fields of view. Furthermore, the tracking performance of labeled multi-Bernoulli (LMB) filter is superior to that of unlabeled filter.