Inverse problem solution techniques as applied to indirect in situ estimation of fish target strength.

In situ indirect methods of fish target strength (TS) estimation are analyzed in terms of the inverse techniques recently applied to the problem in question. The solution of this problem requires finding the unknown probability density function (pdf) of fish target strength from acoustic echoes, which can be estimated by solving the integral equation, relating pdf's of echo variable, target strength, and beam pattern of the echosounder transducer. In the first part of the paper the review of existing indirect in situ TS-estimation methods is presented. The second part introduces the novel TS-estimation methods, viz.: Expectation, Maximization, and Smoothing (EMS), Windowed Singular Value Decomposition (WSVD), Regularization and Wavelet Decomposition, which are compared using simulations as well as actual data from acoustic surveys. The survey data, acquired by the dual-beam digital echosounder, were thoroughly analyzed by numerical algorithms and the target strength and acoustical backscattering length pdf's estimates were calculated from fish echoes received in the narrow beam channel of the echosounder. Simultaneously, the estimates obtained directly from the dual-beam system were used as a reference for comparison of the estimates calculated by the newly introduced inverse techniques. The TS estimates analyzed in the paper are superior to those obtained from deconvolution or other conventional techniques, as the newly introduced methods partly avoid the problem of ill-conditioned equations and matrix inversion.