Inverse scattering problem for optical coherence tomography

We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature

Evaluation of EM-wave propagation in fully three-dimensional atmospheric refractive index distributions

We present a novel numerical method, based on high-frequency localization, for evaluation of electromagnetic-wave propagation through atmospheres exhibiting fully three-dimensional (height, range and cross-range) refractive index variations. This methodology, which is based on localization of Rytov-integration domains to small tubes around geometrical optics paths, can accurately solve three-dimensional propagation problems in orders-of-magnitude shorter computing times than other algorithms available presently. For example, the proposed approach can accurately produce solutions for propagation of ≈20 cm GPS signals across hundreds of kilometers of realistic, three-dimensional atmospheres in computing times on the order of 1 hour in a present-day single-processor workstation, a task for which other algorithms would require, in such single-processor computers, computing times on the order of several months

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers

Reappraisal of SMAP inversion algorithms for soil moisture and vegetation optical depth

International audienceNASA's Soil Moisture Active Passive (SMAP) satellite mission has been providing high-quality global estimates of soil moisture (SM) and vegetation optical depth (VOD) using L-band radiometry since 2015. To date, a variety of retrieval algorithms as well as surface roughness and scattering albedo have been developed. However, a comprehensive evaluation of different algorithms with the new surface parameters across diverse biomes, climates, and terrain slopes is lacking. To narrow down this knowledge gap, here we examine the performance of various existing algorithms, including V-pol Single Channel Algorithms (SCA-V), H-pol Single Channel Algorithms (SCA-H), classic DCA, extended DCA (E-DCA), regularized DCA (RDCA), land parameter retrieval model (LPRM), multi-temporal DCA (MT-DCA), constrained multi-channel algorithm (CMCA), and spatially constrained multi-channel algorithm (S-CMCA). The SM estimates are evaluated against in-situ measurements from the International Soil Moisture Network (ISMN) while VOD estimates are compared with the two-band enhanced vegetation index (EVI2), tree height, and aboveground biomass. This study has led to several important findings: (1) The overall bias, root mean square error (RMSE), and unbiased RMSE (ubRMSE) of SM estimates from different algorithms generally increase with vegetation density while their temporal correlations with in-situ measurements decrease as the terrain slope increases. (2) The divergence between different SM estimates is relatively larger over forested areas than non-forested areas. (3) In terms of temporal correlation with in-situ measurements, the SCA-V and RDCA outperform other algorithms over most land cover types and climates. (4) SCA-H typically underestimates SM more compared to other algorithms across sparsely vegetated areas and most climates. (5) The ubRMSE values demonstrate that all algorithms have close performance when EVI2 is less than 0.3; however, the performance of classic DCA decays notably when EVI2 exceeds 0.3. (6) VOD retrievals from RDCA exhibit improved spatial correlations with EVI2, tree height, and aboveground biomass across the globe compared to other algorithms. Overall, RDCA exhibits a good compromise between the high performance of SM and VOD

A deep neural network based SMAP soil moisture product

In this paper, it is demonstrated that while satellite soil moisture (SM) retrievals often have minimum biases, reanalysis data can capture more temporal variability of SM, especially for non-cropland areas - when validated against in situ measurements. Accordingly, this paper presents a deep neural network (DNN) that utilizes the merits of a suite of existing satellite and reanalysis products to produce a new SM product with minimum (maximum) bias (correlation) - using NASA's Soil Moisture Active Passive (SMAP) data and ERA5 reanalysis. The benchmark of the network is a bias-adjusted SM with maximum correlation with in situ data over each land cover type. The mean of the benchmark data is adjusted to the product that exhibits a minimum bias over each land-cover type. Consistent with the laws of L-band microwave propagation in soil and canopy, the input variables of DNN include polarized SMAP brightness temperatures, incidence angle, vegetation scattering albedo, surface roughness parameter, surface water fraction, effective soil temperatures, bulk density, clay fraction, and vegetation optical depth from the normalized difference vegetation index (NDVI) climatology. The DNN is trained and validated using two years (04/2015-03/2017) of global data and deployed for assessment of its performance from 04/2017 to 03/2021. The testing results against in situ measurements demonstrate that the DNN outputs typically exhibit improved error quality metrics over most land-cover types and climate regimes and can properly capture SM temporal dynamics, beyond each SMAP product across regional to continental scales

Comparison of downscaling techniques for high resolution soil moisture mapping

Soil moisture impacts exchanges of water, energy and carbon fluxes between the land surface and the atmosphere. Passive microwave remote sensing at L-band can capture spatial and temporal patterns of soil moisture in the landscape. Both ESA and NASA have launched L-band radiometers, in the form of the SMOS and SMAP satellites respectively, to monitor soil moisture globally, every 3-day at about 40 km resolution. However, their coarse scale restricts the range of applications. While SMAP included an L-band radar to downscale the radiometer soil moisture to 9 km, the radar failed after 3 months and this initial approach is not applicable to developing a consistent long term soil moisture product across the two missions anymore. Existing optical-, radiometer-, and oversampling-based downscaling methods could be an alternative to the radar-based approach for delivering such data. Nevertheless, retrieval of a consistent high resolution soil moisture product remains a challenge, and there has been no comprehensive intercomparison of the alternate approaches. This research undertakes an assessment of the different downscaling approaches using the SMAPEx-4 field campaign data