Variety Of Inversion Methods Research Articles

Fast Inverse-Scattering Reconstruction for Airborne High-Squint Radar Imagery Based on Doppler Centroid Compensation

Cross-resolution enhancement for airborne high-squint radar (AHSR) imagery is mathematically equivalent to the ill-conditioned problem of inverse-scattering reconstruction. Although a variety of inversion methods with regularization can be introduced to advance the field of AHSR imagery, they turn out to be computationally intensive when extended to 2-D (range and cross-range dimension) image formulation due to the range-by-range calculation for the space-variant inversion operators over the full range swath. To tackle the problem of efficiency, this article presents a low-complexity inverse-scattering strategy. Our underlying idea is to equalize the space-variant Doppler centroid embedded in an inversion operator for a reference range cell using Doppler centroid compensation. With the proposed strategy, the necessary computational complexity required for 2-D AHSR inverse-scattering reconstruction can be significantly reduced by requiring only the calculation of the inversion operator, independently of the number of range cells. Our experimental assessment, conducted using both the simulation and real data, demonstrates that our proposed inverse-scattering strategy offers preferable computational reduction in the task of inverse-scattering reconstruction for 2-D AHSR imagery without resolution loss.

Quantitative implementation of Preisach‐Mayergoyz space to find static and dynamic elastic moduli in rock

In this paper we describe the analysis of quasi‐static stress‐strain data using a Preisach‐Mayergoyz (PM) [after Preisach, 1935; Mayergoyz, 1985] space picture for the elastic behavior of rock. In contrast to the traditional analytic approach to stress strain (an energy density as a function of the strain invariants), the PM space picture reproduces hysteresis and discrete memory seen in the data. In addition, the PM space picture establishes a relationship between experimental data and a number density ρ of microscopic mechanical units within the rock. The density ρ allows us to make quantitative predictions of dynamic elastic properties. Determining ρ from quasi‐static stress‐strain data requires us to solve a highly underdetermined inverse problem. We explore the following three methods of solving the inverse problem: simulated annealing, normal modes, and exponential decay. All three methods are tested on a Berea sandstone data set and found to give an excellent description of stress versus strain. Choosing one method, the normal mode method, we analyze quasi‐static stress‐strain curves on two additional sandstones, namely, another sample of Berea and a sample of Castlegate sandstone. From the density ρ for each sample we predict the dynamic modulus as a function of pressure and the nonlinear elastic constants. For each of these cases the agreement between the predictions based on ρ and experiment is quite good. We establish that PM space provides a quantitative description of the elastic response of a rock and that PM space may be found by a variety of inversion methods.