ESTIMATION OF RADIATION STRESS IN RANDOM WAVE FIELDS

Estimation of Random Fields

Let u(x) = s(x) + n(x) , where s(x) and n(x) are random fields, s(x) is useful signal, n(x) is noise. Assume that s(x) = n(x) = 0 , where the bar stands for mean value. Suppose that the covariance functions R(x, y) := u * (x)u(y) and f (x, y) := u * (x)s(y) are known, where the asterisk stands for complex conjugate. Assume that u(x) is observed in a bounded domain D ⊂ R r of the Euclidean space...

Plane-wave decomposition of spatially random fields.

We investigate the uniqueness of the plane-wave decomposition of temporally deterministic, spatially random fields. Specifically, we consider the decomposition of spatially ergodic and, thus, statistically homogeneous fields. We show that when the spatial power spectrum is injective, the plane waves are the only possible coherent modes. Furthermore, the randomness of such fields originates in t...

Consistent Change Estimation in 2D Random Fields

Radiation Fields for Semilinear Wave Equations

We define the radiation fields of solutions to critical semilinear wave equations in R3 and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the well known support theorem for the Radon transform to this setting and can also be interpreted as a Paley-Wiener theorem for the distorted nonlinear Fourier tran...

Kinetics of scalar wave fields in random media

This paper concerns the derivation of kinetic models for high frequency scalar wave fields propagating in random media. The kinetic equations model the propagation in the phase space of the energy density of a wave field or the correlation function of two wave fields propagating in two possibly different media. Dispersive effects due to e.g. spatial and temporal discretizations, which are model...