Stochastic inverse problem in the radiation of noise
Abstract
The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 December 1978
 Bibcode:
 1978SJAM...35..665C
 Keywords:

 Lagrange Multipliers;
 Noise Generators;
 Point Sources;
 Radiation Sources;
 Stochastic Processes;
 Entropy;
 Functionals;
 Mathematical Models;
 Noise Intensity;
 Sound Generators;
 Acoustics