New regularization method and iteratively reweighted algorithm for sparse vector recovery

Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.

New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation

Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and large errors (up to 15%) in the input data. In both algorithms, the solution is represented as decomposition on special basic functions, which satisfy given a priori information on solution, and this idea allow us significantly to improve the quality of approximate solution and simplify solving the minimization problem. The theoretical details of the algorithms, as well as the results of numerical experiments for proving robustness of the algorithms, are presented.

Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large Noise

A double optimal solution of an n-dimensional system of linear equations Ax=b has been derived in an affine m-dimensional Krylov subspace with m <<n.We further develop a double optimal iterative algorithm(DOIA),with the descent direction z being solved from the residual equation Az=r0 by using its double optimal solution,to solve ill-posed linear problem under large noise.The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||^2=||b-Ax||^2 being reduced by a positive quantity ||Azk||^2 at each iteration step,which is found to be better than those algorithms based on the minimization of the square residual error in an m-dimensional Krylov subspace.In order to tackle the ill-posed linear problem under a large noise,we also propose a novel double optimal regularization algorithm(DORA)to solve it,which is an improvement of the Tikhonov regularization method.Some numerical tests reveal the high performance of DOIA and DORA against large noise.These methods are of use in the ill-posed problems of structural health-monitoring.

Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization Algorithm

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse problems. However, for EIT image reconstruction, the generalized Tikhonov regularization methods may lose the boundary information due to its smoothing operation. In this paper, we propose an iterative Lavrentiev regularization and L-curve-based algorithm to reconstruct EIT images. The regularization parameter should be carefully chosen, but it is often heuristically selected in the conventional regularization-based reconstruction algorithms. So, an L-curve-based optimization algorithm is used for selecting the Lavrentiev regularization parameter. Numerical analysis and simulation results are performed to illustrate EIT image reconstruction. It is shown that choosing the appropriate regularization parameter plays an important role in reconstructing EIT images.

Performance and Complexity Trade-Off between Short-Length Regular and Irregular LDPC

In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.

AN IMPROVED SPARSITY ADAPTIVE MATCHING PURSUIT ALGORITHM FOR COMPRESSIVE SENSING BASED ON REGULARIZED BACKTRACKING

Sparsity Adaptive Matching Pursuit (SAMP) algorithm is a widely used reconstruction algorithm for compressive sensing in the case that the sparsity is unknown. In order to match the sparsity more accurately, we presented an improved SAMP algorithm based on Regularized Backtracking (SAMP-RB). By adapting a regularized backtracking step to SAMP algorithm in each iteration stage, the proposed algorithm can flexibly remove the inappropriate atoms. The experimental results show that SAMP-RB reconstruction algorithm greatly improves SAMP algorithm both in reconstruction quality and computational time. It has better reconstruction efficiency than most of the available matching pursuit algorithms.

Bernoulli-based random undersampling schemes for 2D seismic data regularization

Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing（CS） provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm（SPGL1）, and ten different random seeds. According to the signal-to-noise ratio（SNR） between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.

Source reconstruction for bioluminescence tomography via L_(1/2)regularization

Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem.The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm.In this paper,we present a reconstruction method based on L_(1/2) regularization to enhance sparsity of BLT solution and solve the nonconvex L_(1/2) norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights.To assess the performance of the proposed reconstruction algorithm,simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms,including the weighted interior-point,L1 homotopy,and the Stagewise Orthogonal Matching Pursuit algorithm.Simulation results show that the proposed method yield stable reconstruction results under different noise levels.Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy,multiple-source resolving and image quality.

Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization

Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.

A Regularized Randomized Kaczmarz Algorithm for Large Discrete Ill-Posed Problems

Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.

LightGBM混合模型在乳腺癌诊断中的应用

乳腺癌是最常见的癌症种类之一,且患病率每年仍在上升。在不进行手术活检的情况下,通过分析细胞核的各项指标来预测肿块的良性与否,可以有效地为医生提供辅助诊疗并减少患者的痛苦。为此,提出了一种基于LightGBM算法的乳腺癌诊断模型。使用边界-合成少数类过采样算法(borderline-synthetic minority oversampling technique,Borderline-SMOTE)来改善乳腺癌确诊数据不平衡的问题。在麻雀搜索算法(sparrow search algorithm,SSA)中引入PWLCM混沌映射、全新的惯性权重和纵横交叉算法对其进行改进,再运用改进后的SSA算法对Light-GBM的参数进行自动寻优。由于LightGBM对噪点较为敏感,所以提出了一种OVR-Jacobian正则化方法对LightGBM进行降噪处理。使用改进后的LightGBM混合模型对乳腺癌进行诊断。实验结果表明,提出的混合模型在均方误差、决定系数和交叉验证得分这三个指标上均优于常见的模型,显示出其较好的诊断效果。

基于两步正则化Gauss-Newton迭代算法的ECT图像重建

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

基于自适应动态粒子群优化的RAK-SVD方法

K均值奇异值分解(K-SVD)算法是一种行之有效的地震资料去噪方法,但由于其稀疏分解存在不确定性,需要引入正则项对其改进。为此,在常规粒子群算法的基础上,提出了一种自适应动态粒子群算法优化正则化参数的正则化近似K-SVD(RAK-SVD)去噪方法。首先通过修改字典原子和相关参数,解决了由于常规粒子群算法的惯性参数固定不变,导致后期搜索效率下降的问题;其次将正则化系数引入近似K-SVD(AK-SVD)方法,明显提升了去噪效果;最后利用自适应动态粒子群算法自动优选AK-SVD方法中的正则化参数,提高了稀疏分解的确定性,在对强反射信号进行去噪的同时加强了对弱信号的保护。模型测试和实际应用均表明,该方法有利于弱信号的提取和识别,不仅能够显著改善弱地震信号的去噪效果,还提升了计算效率。该方法具有一定的实际应用价值。

常态化监管与算法分类分级治理模式更新

作为人工智能的核心要素,算法成为了加速新质生产力生成不可或缺的关键技术。在对算法实施分类分级治理的过程中,我国对数字经济监管也走向常态化监管。分类分级理念及原则所涵摄的安全、创新发展及可信可控的价值要求与算法治理的基本目标具有高度一致性,与常态化监管的实践特征具有高度契合性。然而,当前常态化监管思路与算法分类分级治理尚未充分融合。究其原因,主要在于算法治理面临技术迭代与监管模式调整的双重变化,存在治理规则适应技术变化乏力、多元主体治理协同力量不足、治理手段与工具难以适配现实需求等挑战,还难以实现常态化监管与算法分类分级治理的有效融合。为此,文章建议在现行算法安全综合治理格局下,根据常态化监管的理念、原则及架构,对新技术、新业态、新模式发展下算法治理作出调整,转变当前算法治理的基本价值目标、完善治理具体规则、明确治理主体与治理对象及其相应义务与责任、创新治理工具,通过刚性约束与柔性治理相结合、多主体共商共建共治共筑相平衡、丰富治理手段与创新治理工具相同步等举措,不断健全常态化监管下算法分类分级治理模式,提升算法分类分级治理实效,实现算法安全发展、创新发展、规范发展的目标。

基于Criminisi算法的四经绞罗纹样修复研究

文章针对古代罗织物受到诸多因素影响而产生破损、难以提取修复这一问题,提出了一种结合开运算和Criminisi算法的图像修复方法。收集具有规律性特征的四经绞罗传统纹样,用图谱分析法分析最具代表性的菱形纹,使用原算法和开运算改进过的Criminisi算法,对图像进行剪裁,得出掩膜,计算优先权后进行纹样填充,完成了四经绞罗规律型图样的数字化修复。结果表明,经过开运算改进的Criminisi算法弥补了原算法的不足,修复后的图像和原算法修复的相比更加清晰平滑,验证了此算法修复四经绞罗纹样的可行性与可信性,为罗织物的传承和修复提供了较为可靠的方法。

数智时代算法推荐风险的法律治理

算法推荐技术作为国家治理体系和治理能力现代化的关键引擎已被广泛应用,但也引发一系列问题,关乎公民、社会和国家利益。当前算法推荐的法律治理政策呈碎片化,治理效果不彰,迫切需要梳理以构建科学的算法推荐法律治理体系。通过扎根理论研究方法,揭示了五种算法推荐安全风险类型。基于此,构建了主体性法律治理、规则性法律治理和程序性法律治理三种工具,相互协同形成法律协同治理体系,提升算法推荐风险的法律治理水平。展望未来,需持续优化这三种工具的互动机制,规范算法权力行使以实现算法卸责,并推动算法透明度和可解释性的系统性建设。

一种求解低秩矩阵补全的修正加速近端梯度算法

设计适应大规模数据的快速算法是求解低秩矩阵补全的重点。文章改变了加速近端梯度算法的步长,对近似函数的近端最优点和上一迭代点增加了一个仿射组合。通过控制仿射系数,能够使得到的新迭代点有靠近原函数的趋势,进而能在保持算法精度的同时提高算法效率。最后通过相应的数值实验证明了算法的有效性和稳定性。

Dice系数前向预测的快速正交正则回溯匹配追踪算法

为了提高压缩感知重构算法的成功率与重构精度,该文提出基于Dice前向预测的正交正则回溯匹配追踪算法(DLARBOMP)。在该算法中,首先从匹配准则与预选阶段原子选取的角度,利用Dice系数代替原子内积计算相关度,保留原始信号信息的特性,以此选择与残差最匹配的原子,提高算法的重构精度。同时,针对信号重构过程回溯算法的时间过长问题,在每次原子迭代过程中,该文利用正则化选择多个原子而非单个原子,实现重构精度与重构时间的平衡。最后,通过稀疏1维信号与2维图像信号重构的实验结果,显示了所提DLARBOMP算法在1维信号重构时兼顾了性能与效率,在2维压缩图像信号重构时提高其峰值信噪比(PSNR),优于正交匹配追踪(OMP)及其最新改进贪婪类算法。

三维大地电磁测深阶段式自适应正则化反演

如何合理地确定正则化因子是地球物理正则化反演领域的研究热点。阶段式自适应算法可以充分发挥模型稳定器的作用,提高反演结果的稳定性,但是该算法仅在一维、二维大地电磁测深(Magnetotelluric,MT)反演中得以实现。目前,三维MT反演正在快速发展,基于此,本文将阶段式自适应正则化算法引入三维MT正则化反演,按照“阶段”而不是“迭代次数”自适应地调整正则化因子的取值,进而观察反演结果的变化。本文设计单块体和双块体模型试验,并特意设置了较大的迭代次数,进而观察反演结果随反演进程的变化情况。模型试验表明:阶段式自适应算法是适用于三维MT正则化反演的,该算法在反演的后期可以更好地保持解的稳定,故此,从解的稳定性这个角度去考量正则化因子的选择是一种值得探索的方向。

用于皮肤病激光治疗的脉冲光热辐射模型

针对皮肤病激光治疗过程中生物组织内部温度分布与形态测量困难、医生凭借经验选取治疗参数导致疗效不佳等问题,建立了利用脉冲光热辐射法(PPTR)重建皮肤结构,并智能化选取激光参数开展辅助治疗的理论模型。采用基于自定义截断参数选取方法的截断奇异值分解法、基于L曲线法选取正则化参数的Tikhonov正则化法和给定迭代次数的共轭梯度法这3种逆算法进行仿真计算,建立误差评估函数,分析对比了不同表皮层厚度、患病层厚度及深度的重建效果,同时制作皮肤仿体进行离体实验,并以此为依据开展了鲜红斑痣临床治疗的应用研究。结果表明:3种逆算法的综合性能评价指数由高到低依次为0.066、0.082、0.126,验证了其在鲜红斑痣血管层常见深度范围内的重建效果均能保持较高精度;体外实验结果和临床应用验证了所提出的PPTR模型可用于求解表皮、病变层等组织的温升分布、厚度、位置等信息,且重建结果的精度能够满足治疗需求。该模型及研究结果可为激光治疗过程中参数的选取提供定量化指导。