Related papers: Development of hp-inverse model by using generaliz…
Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse…
Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model…
Inverse problems in imaging are ill-posed, leading to infinitely many solutions consistent with the measurements due to the non-trivial null-space of the sensing matrix. Common image priors promote solutions on the general image manifold,…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A=CR$ to establish a unifying framework for generalized and randomized matrix inverses. This analysis is rooted in first principles, focusing on the…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
We propose a method to fit arbitrarily accurate blendshape rig models by solving the inverse rig problem in realistic human face animation. The method considers blendshape models with different levels of added corrections and solves the…
This work focuses on the problem of reconstructing a 3D human body mesh from a given 2D image. Despite the inherent ambiguity of the task of human mesh recovery, most existing works have adopted a method of regressing a single output. In…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
An approach is presented for the inversion of simulated and experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…