scholarly journals Integral equations of the first kind, inverse problems and regularization: a crash course

2007 ◽  
Vol 73 ◽  
pp. 012001 ◽  
Author(s):  
C W Groetsch
Keyword(s):  
Inverse Problems ◽  
Integral Equations

scholarly journals Dynamic near-field microwave diagnostics of lungs.

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
L.A. Bokeria ◽  
◽  
T.T. Kakuchaya ◽  
A.M. Kuular ◽  
Ye.S. Maksimovitch ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Inverse Problems ◽  
Integral Equations ◽  
Near Field ◽  
Experimental Studies ◽  
Heart Activity ◽  
Blood Content ◽  
Air Content ◽  
Microwave Diagnostics ◽  
Biomedical Diagnostics

Results of theoretical and experimental studies of the method of the near-field microwave tomography of the thorax are presented. Integral equations of inverse tomography problem of 3D blood- and air content inhomogeneities by data of multisensory measurements are obtained. Methods of air and blood content profiling in processes of breathing and heart activity by data of bistatic measurements of the scattered signal are proposed and solving algorithms of inverse problems are studied in the numerical simulation. Multifrequency and pulse measurements of scattered signals are carried out in processes of cardiorespiratory activity. By data of bistatic measurements of scattered signals parameters from the thorax, profiling relative air- and blood content profiles has been realized. Application possibilities of the method in the biomedical diagnostics are considered.

scholarly journals DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION

2006 ◽  
Vol 04 (01) ◽  
pp. 81-99 ◽  
Author(s):  
ERNESTO DE VITO ◽  
LORENZO ROSASCO ◽  
ANDREA CAPONNETTO
Keyword(s):  
Inverse Problems ◽  
Error Analysis ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Tikhonov Regularization ◽  
Discretization Error ◽  
Learning From Examples ◽  
Carleman Operator

We study the discretization of inverse problems defined by a Carleman operator. In particular, we develop a discretization strategy for this class of inverse problems and we give a convergence analysis. Learning from examples, as well as the discretization of integral equations, can be analyzed in our setting.

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