Tikhonov regularization
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Isotropic Total Variation Regularization of Displacements in Parametric Image Registration Open
Spatial regularization is essential in image registration, which is an ill-posed problem. Regularization can help to avoid both physically implausible displacement fields and local minima during optimization. Tikhonov regularization (squar…
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The distribution of ammonia on Jupiter from a preliminary inversion of Juno microwave radiometer data Open
The Juno microwave radiometer measured the thermal emission from Jupiter's atmosphere from the cloud tops at about 1 bar to as deep as a hundred bars of pressure during its first flyby over Jupiter (PJ1). The nadir brightness temperatures …
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Distribution (function) of relaxation times, successor to complex nonlinear least squares analysis of electrochemical impedance spectroscopy? Open
Electrochemical impedance spectroscopy (EIS) and complex nonlinear least squares (CNLS) analysis with an equivalent circuit (EqC) has been the standard research tool in Solid State Electrochemistry for many decades. With an ever increasing…
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System Identification: A Machine Learning Perspective Open
Estimation of functions from sparse and noisy data is a central theme in machine learning. In the last few years, many algorithms have been developed that exploit Tikhonov regularization theory and reproducing kernel Hilbert spaces. These …
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Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method Open
In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel $$RC$$ circuit and two parallel $$RC$$ circuits connected in series, experime…
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Electrochemical Impedance Imaging via the Distribution of Diffusion Times Open
We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit…
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Seismic waveform inversion best practices: regional, global and exploration test cases Open
Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to…
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Back-propagation neural network-based reconstruction algorithm for diffuse optical tomography Open
Diffuse optical tomography (DOT) is a promising noninvasive imaging modality and is capable of providing functional characteristics of biological tissue by quantifying optical parameters. The DOT image reconstruction is ill-posed and ill-c…
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Bayesian regularization networks for micropolar ternary hybrid nanofluid flow of blood with homogeneous and heterogeneous reactions: Entropy generation optimization Open
This study aims to analyze a Bayesian regularization backpropagation algorithm for micropolar ternary hybrid nanofluid flow over curved surfaces with homogeneous and heterogeneous reactions, Joule heating and viscous dissipation. The terna…
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Deep neural network-based bandwidth enhancement of photoacoustic data Open
Photoacoustic (PA) signals collected at the boundary of tissue are always band-limited. A deep neural network was proposed to enhance the bandwidth (BW) of the detected PA signal, thereby improving the quantitative accuracy of the reconstr…
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BOREAS – a new MAX-DOAS profile retrieval algorithm for aerosols and trace gases Open
We present a new MAX-DOAS profiling algorithm for aerosols and trace gases, BOREAS, which utilizes an iterative solution method including Tikhonov regularization and the optimal estimation technique. The aerosol profile retrieval is based …
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Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning Open
Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 a…
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Total Variation Regularization With Split Bregman-Based Method in Magnetic Induction Tomography Using Experimental Data Open
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PET image reconstruction using multi-parametric anato-functional priors Open
In this study, we investigate the application of multi-parametric anato-functional (MR-PET) priors for the maximum a posteriori (MAP) reconstruction of brain PET data in order to address the limitations of the conventional anatomical prior…
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Reconstructing the electrical structure of dust storms from locally observed electric field data Open
While the electrification of dust storms is known to substantially affect the lifting and transport of dust particles, the electrical structure of dust storms and its underlying charge separation mechanisms are largely unclear. Here we pre…
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3-D inversion of magnetic data based on the L1–L2 norm regularization Open
Magnetic inversion is one of the popular methods to obtain information about the subsurface structure. However, many of the conventional methods have a serious problem, that is, the linear equations to be solved become ill-posed, under-det…
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Finding the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis Open
The distribution of relaxation times (DRT) method allows the direct interpretation of electrochemical impedance data, yielding an increased resolution in the frequency domain. Calculating the DRT from experimental impedance spectra, howeve…
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Combined neural network/Phillips–Tikhonov approach to aerosol retrievals over land from the NASA Research Scanning Polarimeter Open
In this paper, an algorithm for the retrieval of aerosol and land surface properties from airborne spectropolarimetric measurements – combining neural networks and an iterative scheme based on Phillips–Tikhonov regularization – is describe…
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Fractional Regularization to Improve Photoacoustic Tomographic Image Reconstruction Open
Photoacoustic tomography involves reconstructing the initial pressure rise distribution from the measured acoustic boundary data. The recovery of the initial pressure rise distribution tends to be an ill-posed problem in the presence of no…
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Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study Open
The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different …
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A new regularization method for dynamic load identification Open
Dynamic forces are very important boundary conditions in practical engineering applications, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. Moreover, there are many applications in whi…
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Combining the Distribution of Relaxation Times from EIS and Time-Domain Data for Parameterizing Equivalent Circuit Models of Lithium-Ion Batteries Open
Equivalent circuit models (ECMs) are a widely used modeling approach for lithium-ion batteries in engineering applications. The RC elements, which display the dynamic loss processes of the cell, are usually parameterized by fitting the ECM…
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Hybrid and iteratively reweighted regularization by unbiased predictive\n risk and weighted GCV for projected systems Open
Tikhonov regularization for projected solutions of large-scale ill-posed\nproblems is considered. The Golub-Kahan iterative bidiagonalization is used to\nproject the problem onto a subspace and regularization then applied to find a\nsubspa…
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Verification of a variational source condition for acoustic inverse medium scattering problems Open
This paper is concerned with the classical inverse scattering problem to\nrecover the refractive index of a medium given near or far field measurements\nof scattered time-harmonic acoustic waves. It contains the first rigorous proof\nof (l…
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Non-Negative Iterative Convex Refinement Approach for Accurate and Robust Reconstruction in Cerenkov Luminescence Tomography Open
Cerenkov luminescence tomography (CLT) is a promising imaging tool for obtaining three-dimensional (3D) non-invasive visualization of the in vivo distribution of radiopharmaceuticals. However, the reconstruction performance remains unsatis…
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Data Unfolding Methods in High Energy Physics Open
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods…
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An Improved GPS-Inferred Seasonal Terrestrial Water Storage Using Terrain-Corrected Vertical Crustal Displacements Constrained by GRACE Open
Based on a geophysical model for elastic loading, the application potential of Global Positioning System (GPS) vertical crustal displacements for inverting terrestrial water storage has been demonstrated using the Tikhonov regularization a…
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MEG Connectivity and Power Detections with Minimum Norm Estimates Require Different Regularization Parameters Open
Minimum Norm Estimation (MNE) is an inverse solution method widely used to reconstruct the source time series that underlie magnetoencephalography (MEG) data. MNE addresses the ill-posed nature of MEG source estimation through regularizati…
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Investigation of gas–solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique Open
Electrical capacitance tomography (ECT) provides a non‐intrusive means to visualize cross‐sectional material distribution of gas–solid bubbling fluidized beds. Successful application of ECT strongly depends on the image reconstruction algo…
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An inverse random source problem in a stochastic fractional diffusion equation Open
In this work the authors consider an inverse source problem the stochastic fractional diffusion equation. The interested inverse problem is to reconstruct the unknown spatial functions f and g (the latter up to the sign) in the source by t…