相关论文: A data-assisted two-stage method for the inverse r…
We implemented a simple method for early detection in this research. The implemented methods are plotting the given mat files and analyzing scalogram images generated by performing Continuous Wavelet Transform (CWT) on the samples. Also,…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
The spatial dependent unknown acoustic source is reconstructed according noisy multiple frequency data on a remote closed surface. Assume that the unknown function is supported on a bounded domain. To determine the support, we present a…
Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…
Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…
Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges…
The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…
In this paper we introduce a new method called the Dirac Assisted Tree (DAT) method, which can handle 1D heterogeneous Helmholtz equations with arbitrarily large variable wave numbers. DAT breaks an original global problem into many…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual…
Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…