Positive regularised solutions in electromagnetic inverse scattering

Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data.

Applied Inverse Problems in Optics

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Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

SVD for linear inverse problems

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Stability Problems in Inverse Diffraction

Inverse diffraction consists in determining the field distribution on a boundary surface from the knowledge of the distribution on a surface situated within the domain where the wave propagates. This problem is a good example for illustrating the use of least-squares methods (also called regularization methods) for solving linear ill-posed inverse problem. We focus on obtaining error bounds For regularized solutions and show that the stability of the restored field far from the boundary surface is quite satisfactory: the error is proportional to ∊(ðŗ‚ ≃ 1) ,ðŗœ being the error in the data (Hölder continuity). However, the error in the restored field on the boundary surface is only proportional to an inverse power of │In∊│ (logarithmic continuity). Such a poor continuity implies some limitations on the resolution which is achievable in practice. In this case, the resolution limit is seen to be about half of the wavelength. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.

Superresolution in linear inverse problems

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Performance evaluation of a distributed algorithm for an inverse heat conduction problem

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Forward and inverse transport of particulate matter and gaseous pollutants affecting the region bordering the English Channel

The ATTMA "Aerosol Transport in the Trans-Manche Atmosphere" project investigates the transportation and dispersion of air pollutants across the English Channel, in collaboration with local authorities and other Universities in Southern England and Northern France. The research is concerned with both forward and inverse (receptor based) tracking. Two alternative dispersion simulation methods are used: (a) Lagrangian Particle Dispersion (LPD) models, (b) Eulerian Finite Volume type models. This paper is concerned with part (a), the simulations based on LPD models. Two widely applied LPD models are used and compared. Since in many observed episodes the source of pollution is traced outside the region of interest, long range, trans-continental transport is also investigated.

Parallel genetic algorithms for the solution of inverse heat conduction problems

A parallel genetic algorithm (PGA) is proposed for the solution of two-dimensional inverse heat conduction problems involving unknown thermophysical material properties. Experimental results show that the proposed PGA is a feasible and effective optimization tool for inverse heat conduction problems

Carbon fluxes and pelagic ecosystem dynamics near two western Antarctic Peninsula Adélie penguin colonies: an inverse model approach

An inverse food-web model for the western Antarctic Peninsula (WAP) pelagic food web was constrained with data from Palmer Long Term Ecological Research (PAL-LTER) project annual austral summer sampling cruises. Model solutions were generated for 2 regions with Adelie penguin Pygoscelis adeliae colonies presenting different population trends (a northern and a southern colony) for a 12 yr period (1995-2006). Counter to the standard paradigm, comparisons of carbon flow through bacteria, microzooplankton, and krill showed that the diatom-krill-top predator food chain is not the dominant pathway for organic carbon exchanges. The food web is more complex, including significant contributions by microzooplankton and the microbial loop. Using both inverse model results and network indices, it appears that in the northern WAP the food web is dominated by the microbial food web, with a temporal trend toward its increasing importance. The dominant pathway for the southern WAP food web varies from year to year, with no detectable temporal trend toward dominance of microzooplankton versus krill. In addition, sensitivity analyses indicated that the northern colony of Adelie penguins, whose population size has been declining over the past 35 yr, appears to have sufficient krill during summer to sustain its basic metabolic needs and rear chicks, suggesting the importance of other processes in regulating the Adelie population decline.

Ecological controls on biogeochemical fluxes in the western Antarctic Peninsula studied with an inverse foodweb model

Sea ice in the western Antarctic Peninsula (WAP) region is both highly variable and rapidly changing. In the Palmer Station region, the ice season duration has decreased by 92 d since 1978. The sea-ice changes affect ocean stratification and freshwater balance and in turn impact every component of the polar marine ecosystem. Long-term observations from the WAP nearshore and offshore regions show a pattern of chlorophyll (Chl) variability with three to five years of negative Chl anomalies interrupted by one or two years of positive anomalies (high and low Chl regimes). Both field observations and results from an inverse food-web model show that these high and low Chl regimes differed significantly from each other, with high primary productivity and net community production (NCP) and other rates associated with the high Chl years and low rates with low Chl years. Gross primary production rates (GPP) averaged 30 mmolC.m-2.d-1 in the low Chl years and 100 mmolC.m-2.d-1 in the high Chl years. Both large and small phytoplankton were more abundant and more productive in high Chl years than in low Chl years. Similarly, krill were more important as grazers in high Chl years, but did not differ from microzooplankton in high or low Chl years. Microzooplankton did not differ between high and low Chl years. Net community production differed significantly between high and low Chl years, but mobilized a similar proportion of GPP in both high and low Chl years. The composition of the NCP was uniform in high and low Chl years. These results mphasize the importance of microbial components in the WAP plankton system and suggest that food webs dominated by small phytoplankton can have pathways that funnel production into NCP, and likely, export.