相关论文: Inversion of multiconfiguration complex EMI data w…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
Inverse design of metasurfaces for the joint optimization of optical modulation and algorithmic decoding in computational optics presents significant challenges, especially in applications such as hyperspectral imaging. We introduce a…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
Sub-sampling is applied to simulated $T_1$-$D$ NMR signals and its influence on inversion performance is evaluated. For this different levels of sub-sampling were employed ranging from the fully sampled signal down to only less than two…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Full waveform inversion (FWI) enables us to obtain high-resolution velocity models of the subsurface. However, estimating the associated uncertainties in the process is not trivial. Commonly, uncertainty estimation is performed within the…
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f \in \C^N$ and a randomly chosen set of frequencies $\Omega$ of mean size $\tau N$. Is it possible to…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…
Full waveform inversion (FWI) is a nonlinear PDE constrained optimization problem, which seeks to estimate constitutive parameters of a medium such as phase velocity, density, and anisotropy, by fitting waveforms. Attenuation is an…
The interaction between the foundation structures and the soil has been developed for many engineering applications. For the determination of the stress in foundation structure it is needed to determine the influence of the stiffness of…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology…
Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models. In many cases these parameter fields reflect different attributes of a single…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…