Inverse Problems最新文献

Joint sparse optimization: Lower-order regularization method and application in cell fate conversion 联合稀疏优化：低阶正则化方法及其在细胞命运转换中的应用

Inverse Problems Pub Date : 2024-07-10 DOI: 10.1088/1361-6420/ad617d

Yaohua Hu, Xinlin Hu, C. Yu, Jing Qin

{"title":"Joint sparse optimization: Lower-order regularization method and application in cell fate conversion","authors":"Yaohua Hu, Xinlin Hu, C. Yu, Jing Qin","doi":"10.1088/1361-6420/ad617d","DOIUrl":"https://doi.org/10.1088/1361-6420/ad617d","url":null,"abstract":"\u0000 Multiple measurement signals are commonly collected in practical applications, and joint sparse optimization adopts the synchronous effect within multiple measurement signals to improve model analysis and sparse recovery capability. In this paper, we investigate the joint sparse optimization problem via $ell_{p,q}$ regularization ($0le q le 1 le p$) in three aspects: theory, algorithm and application. In the theoretical aspect, we introduce a weak notion of joint restricted Frobenius norm condition associated with the $ell_{p,q}$ regularization, and apply it to establish an oracle property and a recovery bound for the $ell_{p,q}$ regularization of joint sparse optimization problem. In the algorithmic aspect, we apply the well-known proximal gradient algorithm to solve the $ell_{p,q}$ regularization problems, provide analytical formulas for proximal subproblems of certain specific $ell_{p,q}$ regularizations, and establish the global convergence and linear convergence rate of the proximal gradient algorithm under some mild conditions. More importantly, we propose two types of proximal gradient algorithms with the truncation technique and the continuation technique, respectively, and establish their convergence to the ground true joint sparse solution within a tolerance relevant to the noise level and the recovery bound under the assumption of restricted isometry property. In the aspect of application, we develop a novel method, based on joint sparse optimization with lower-order regularization and proximal gradient algorithm, to infer the master transcription factors for cell fate conversion, which is a powerful tool in developmental biology and regenerative medicine. Numerical results indicate that the novel method facilitates fast identification of master transcription factors, give raise to the possibility of higher successful conversion rate and in the hope of reducing biological experimental cost.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"32 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141659255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees 使用基于加权表达树的可解释机器学习方法，从时间序列生物数据中推断动态模型

Inverse Problems Pub Date : 2024-07-09 DOI: 10.1088/1361-6420/ad60f1

Yu Zhou, Xiufen Zou

{"title":"Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees","authors":"Yu Zhou, Xiufen Zou","doi":"10.1088/1361-6420/ad60f1","DOIUrl":"https://doi.org/10.1088/1361-6420/ad60f1","url":null,"abstract":"\u0000 The growing time-series data make it possible to glimpse the hidden dynamics in various fields. However, developing a computational toolbox with high interpretability to unveil the interaction dynamics from data remains a crucial challenge. Here, we propose a new computational approach called Automated Dynamical Model Inference based on Expression Trees (ADMIET), in which the machine learning algorithm, the numerical integration of ordinary differential equations and the interpretability from prior knowledge are embedded into the symbolic learning scheme to establish a general framework for revealing the hidden dynamics in time-series data. ADMIET takes full advantage of both machine learning algorithm and expression tree. Firstly, we translate the prior knowledge into constraints on the structure of expression tree, reducing the search space and enhancing the interpretability. Secondly, we utilize the proposed adaptive penalty function to ensure the convergence of gradient descent algorithm and the selection of the symbols. Compared to gene expression programming, ADMIET exhibits its remarkable capability in function fitting with higher accuracy and broader applicability. Moreover, ADMIET can better fit parameters in nonlinear forms compared to regression methods. Furthermore, we apply ADMIET to two typical biological systems and one real data with different prior knowledge to infer the dynamical equations. The results indicate that ADMIET can not only discover the interaction relationships but also provide accurate estimates of the parameters in the equations. These results demonstrate ADMIET's superiority in revealing interpretable dynamics from time-series biological data.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"85 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On bias and its reduction via standardization in discretized electromagnetic source localization problems 关于离散化电磁源定位问题中的偏差及其通过标准化减少偏差的问题

Inverse Problems Pub Date : 2024-07-04 DOI: 10.1088/1361-6420/ad5f53

Joonas Lahtinen

引用次数: 1

Special issue on optimization and learning methods for inverse problems in microscopy: in memory of Mario Bertero 显微镜逆问题的优化和学习方法特刊：纪念马里奥-贝特罗

Inverse Problems Pub Date : 2024-07-01 DOI: 10.1088/1361-6420/ad575d

L. Calatroni, Simone Rebegoldi, Valeria Ruggiero

引用次数: 0

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT) 利用磁共振电阻抗断层扫描（MREIT）重建各向同性电导的稳定性

Inverse Problems Pub Date : 2024-05-17 DOI: 10.1088/1361-6420/ad4d19

Haiyang Wang, Yizhuang Song

{"title":"Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)","authors":"Haiyang Wang, Yizhuang Song","doi":"10.1088/1361-6420/ad4d19","DOIUrl":"https://doi.org/10.1088/1361-6420/ad4d19","url":null,"abstract":"\u0000 Magnetic resonance electrical impedance tomography (MREIT) is a high-resolution imaging modality that aims to reconstruct the objects' conductivity distributions at low frequency using the measurable $z$-th component of the magnetic flux density obtained from an MRI scanner. Traditional reconstruction algorithms in MREIT use two data subject to two linearly independent current densities. However, the temporal resolution of such a MREIT image is relatively low. Recently, a single current MREIT has been proposed to improve the temporal resolution. Even though a series of reconstruction algorithms have been proposed in the last two decades, the theoretical studies of MREIT are still quite limited. This paper presents the stability theorems for two datum and a single data-based isotropic conductivity reconstruction using MREIT. Using the regularity theory of elliptic partial differential equations, we prove that the only instability in the inverse problem of MREIT comes from taking the second-order derivative of the measured data $B_z$, the $z$-th component of the magnetic flux density. To get a stable reconstruction from the noisy $B_z$ data, we note that the edge structure of $nabla B_z$ reveals the edge features in the unknown conductivity and provides an edge-preserving denoising approach for the $nabla B_z$ data. We use a modified Shepp-Logan phantom model to validate the proposed theory and the denoising approach.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"21 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniqueness and numerical inversion in bioluminescence tomography with time-dependent boundary measurement 具有时变边界测量功能的生物发光层析成像中的唯一性和数值反演

Inverse Problems Pub Date : 2024-05-10 DOI: 10.1088/1361-6420/ad49cb

Rongfang Gong, Xinran Liu, Jun Shen, Qin Huang, Chunlong Sun, Ye Zhang

{"title":"Uniqueness and numerical inversion in bioluminescence tomography with time-dependent boundary measurement","authors":"Rongfang Gong, Xinran Liu, Jun Shen, Qin Huang, Chunlong Sun, Ye Zhang","doi":"10.1088/1361-6420/ad49cb","DOIUrl":"https://doi.org/10.1088/1361-6420/ad49cb","url":null,"abstract":"\u0000 In the paper, an inverse source problem in bioluminescence tomography (BLT) is investigated. BLT is a method of light imaging and offers many advantages such as sensitivity, cost-effectiveness, high signal-to-noise ratio and non-destructivity. It thus has promising prospects for many applications such as cancer diagnosis, drug discovery and development as well as gene therapies. In the literature, BLT is extensively studied based on the (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is reconstructed and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a novel dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, iterative inversion algorithms under the framework of regularizing schemes are introduced and applied to reconstruct the smooth and non-smooth sources. We discretize the regularization functional with the finite element method and give the convergence rate of numerical solutions. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithms.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On dynamical system modeling of Learned Primal-Dual with a linear operator $mathcal{K}$: Stability and convergence properties 关于具有线性算子 $mathcal{K}$ 的 Learned Primal-Dual 的动力学系统建模：稳定性与收敛性

Inverse Problems Pub Date : 2024-05-10 DOI: 10.1088/1361-6420/ad49ca

Jinshu Huang, Yiming Gao, Chunlin Wu

{"title":"On dynamical system modeling of Learned Primal-Dual with a linear operator $mathcal{K}$: Stability and convergence properties","authors":"Jinshu Huang, Yiming Gao, Chunlin Wu","doi":"10.1088/1361-6420/ad49ca","DOIUrl":"https://doi.org/10.1088/1361-6420/ad49ca","url":null,"abstract":"\u0000 Learned Primal-Dual (LPD) is a deep learning based method for composite optimization problems that is based on unrolling/unfolding the primal-dual hybrid gradient algorithm. While achieving great successes in applications, the mathematical interpretation of LPD as a truncated iterative scheme is not necessarily sufficient to fully understand its properties. In this paper, we study the LPD with a general linear operator. We model the forward propagation of LPD as a system of difference equations and a system of differential equations in discrete- and continuous-time settings (for primal and dual variables/trajectories), which are named discrete-time LPD and continuous-time LPD, respectively. Forward analyses such as stabilities and the convergence of the state variables of the discrete-time LPD to the solution of continuous-time LPD are given. Moreover, we analyze the learning problems with/without regularization terms of both discrete-time and continuous-time LPD from the optimal control viewpoint. We prove convergence results of their optimal solutions with respect to the network state initialization and training data, showing in some sense the topological stability of the learning problems. We also establish convergence from the solution of the discrete-time LPD learning problem to that of the continuous-time LPD learning problem through a piecewise linear extension, under some appropriate assumptions on the space of learnable parameters. This study demonstrates theoretically the robustness of the LPD structure and the associated training process, and can induce some future research and applications.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":" 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140990924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Inverse stable reconstruction of 3 coefficients for the heterogeneous Maxwell equations by finite number of partial interior observations 通过有限数量的部分内部观测反向稳定重建异质麦克斯韦方程的 3 个系数

Inverse Problems Pub Date : 2024-05-03 DOI: 10.1088/1361-6420/ad473a

Michel Cristofol, Masahiro Yamamoto

引用次数: 0

Uniqueness results for inverse source problems for semilinear elliptic equations 半线性椭圆方程反源问题的唯一性结果

Inverse Problems Pub Date : 2024-03-06 DOI: 10.1088/1361-6420/ad3088

Tony Liimatainen, Yi-Hsuan Lin

{"title":"Uniqueness results for inverse source problems for semilinear elliptic equations","authors":"Tony Liimatainen, Yi-Hsuan Lin","doi":"10.1088/1361-6420/ad3088","DOIUrl":"https://doi.org/10.1088/1361-6420/ad3088","url":null,"abstract":"\u0000 We study inverse source problems associated to semilinear elliptic equations of the form [ Delta u(x)+a(x,u)=F(x) ] on a bounded domain $Omegasubset R^n$, $ngeq 2$. We show that it is possible to use nonlinearity to recover both the source $F$ and the nonlinearity $a(x,u)$ simultaneously and uniquely for a class of nonlinearities. This is in contrast to inverse source problems for linear equations, which always have a natural (gauge) symmetry that obstructs tbr{the} unique recovery of the source. The class of nonlinearities for which we can uniquely recover the source and nonlinearity, tbr{includes} a class of polynomials, which we characterize, and exponential nonlinearities. For general nonlinearities $a(x,u)$, we recover the source $F(x)$ and the Taylor coefficients $p_u^ka(x,u)$ up to a gauge symmetry. We recover general polynomial nonlinearities up to tbr{the gauge} symmetry. Our results tbr{also} generalize results of cite{FO19,LLLS2019partial} by removing the assumption that $uequiv 0$ is a solution. To prove our results, we consider linearizations around possibly large solutions. Our results can lead to new practical applications, because we show that many practical models do not have the obstruction for unique recovery that has restricted the applicability of inverse source problems for linear models.","PeriodicalId":508687,"journal":{"name":"Inverse Problems","volume":"46 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140077716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Consistency of the Bayes method for the inverse scattering problem 贝叶斯法在反向散射问题上的一致性

Inverse Problems Pub Date : 2024-03-06 DOI: 10.1088/1361-6420/ad3089

Takashi Furuya, Pu-Zhao Kow, Jenn-Nan Wang

引用次数: 1