Search results for "Inverse problem"
showing 10 items of 163 documents
Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties
2019
International audience; In inverse problems, the use of an l(12) analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good be…
Retrieval of atmospheric CH4profiles from Fourier transform infrared data using dimension reduction and MCMC
2016
We introduce an inversion method that uses dimension reduction for the retrieval of atmospheric methane (CH4) profiles. Uncertainty analysis is performed using the Markov chain Monte Carlo (MCMC) statistical estimation. These techniques are used to retrieve CH4 profiles from the ground-based spectral measurements by the Fourier Transform Spectrometer (FTS) instrument at Sodankyla (67.4 degrees N, 26.6 degrees E), Northern Finland. The Sodankyla FTS is part of the Total Carbon Column Observing Network (TCCON), a global network that observes solar spectra in near-infrared wavelengths. The high spectral resolution of the data provides approximately 3 degrees of freedom about the vertical struc…
Inverse problem for tripotential measures in the study of buried cavities
1996
This paper presents a solution to the inverse electrical problem for the interpretation of apparent resistivity anomalies due to empty buried cavities of quasi-spherical shape when tripotential measures are carried out. The anomalies of the apparent resistivities ra,rb andrg,and the composed resistivitiesrmand rt were previously calculated for a sufficient class of spherical models of resistivity anomalies. Then, for the whole class of models, some functionals of spatial distribution of the apparent and composed resistivity were identified and analyzed. They represent the average characteristics of the anomalies and, depending in a simple way on the fundamental parameters of the sources of …
An adaptive-PCA algorithm for reflectance estimation from color images
2008
This paper deals with the problem of spectral reflectance estimation from color camera outputs. Because the reconstruction of such functions is an inverse problem, stabilizing the reconstruction process is highly desirable. One way to do this is to decompose reflectance function on a basis functions like PCA. The present work proposes an algorithm making PCA adaptive in reflectance estimation from a color camera output. We propose to adapt the PCA basis derivation by selecting, for each sample, the more relevant elements from the training set elements. The adaptivity criterion is achieved by a likelihood measurement. Finally, the spectral reflectance estimation results are evaluated with th…
A Review of Mathematical and Computational Methods in Cancer Dynamics.
2022
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the si…
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
Electrocardiographic Imaging for Atrial Fibrillation: A Perspective From Computer Models and Animal Experiments to Clinical Value
2021
[EN] Electrocardiographic imaging (ECGI) is a technique to reconstruct non-invasively the electrical activity on the heart surface from body-surface potential recordings and geometric information of the torso and the heart. ECGI has shown scientific and clinical value when used to characterize and treat both atrial and ventricular arrhythmias. Regarding atrial fibrillation (AF), the characterization of the electrical propagation and the underlying substrate favoring AF is inherently more challenging than for ventricular arrhythmias, due to the progressive and heterogeneous nature of the disease and its manifestation, the small volume and wall thickness of the atria, and the relatively large…
Some Relationships between Molecular Energy-Topology and Symmetry
2001
Molecular Topology (M.T.) has demonstrated its efficiency in the prediction of many experimental parameters. The application of the topological indices to the prediction of pharmacological properties, and, above all, to its inverse problem, the drug design, is particularly interesting [1,2]. Several attempts to explain the reasons of such efficiency have been carried out [3,4]. So far, we are not close to a definitive answer.
The linearized Calderón problem on complex manifolds
2019
International audience; In this note we show that on any compact subdomain of a Kähler manifold that admits sufficiently many global holomorphic functions , the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of Kähler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot by treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holo-morphic functions with approximately prescribed critical points.…
Identification of small inhomogeneities: Asymptotic factorization
2007
We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral …