Discrete Scatterer Model Research Articles

Sensitivity Study of X-Band Multiparametric SAR Data From Cabbage Fields

To make polarimetric synthetic aperture radar (SAR) accessible to mainstream applications, the true composition ratio of scattering mechanisms within a radar backscatter must be accurately identified. To validate polarimetric SAR decomposition techniques, a novel multiparametric SAR observation combined with a theoretical model simulation has been applied to rice paddies having simple vegetation structure on smooth and flat surfaces, where the surface scattering was small. In this article, cabbage fields in Miura city in Japan were selected as outdoor-grown vegetables, so the effect of exposed ground surfaces must be taken into account. In combination with the multiparametric SAR observation, a dominant scattering mechanism is reliably isolated through the theoretical characterization of the data by a discrete scatterer model (DSM). Suppressing unnecessary effects by row structures of the crop field, the volume scattering from cabbage leaves is identified as a dominant scattering mechanism over most incidence angles. On the other hand, the surface scattering is dominant for copolarizations only at small incidence angles. The analysis also indicates the possibility that greater soil moisture could be kept by roots of mature cabbages. To demonstrate the validation of polarimetric decomposition by the results, a popular three-component decomposition was applied to the observation. Differences between the decomposition and the simulation results were analytically explained by features of the backscatter from cabbage fields. Model-based polarimetric decompositions shall be improved through this approach.

Estimation of Vegetation Structure Parameters From SMAP Radar Intensity Observations

In this article, we present a multipolarimetric estimation approach for two model-based vegetation structure parameters (shape A and orientation distribution ψ of the main canopy elements). The approach is based on a reduced observation set of three incoherent (no phase information) polarimetric backscatter intensities (|S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HH</sub> | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , |S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HV</sub> | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and |S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VV</sub> | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) combined with a two-parameter (A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> and ψ) discrete scatterer model of vegetation. The objective is to understand whether this confined set of observations contains enough information to estimate the two vegetation structure parameters from the L-band radar signals. In order to disentangle soil and vegetation scattering influences on these signals and ultimately perform a vegetation only retrieval of vegetation shape A and orientation distribution ψ, we use the subpixel spatial heterogeneity expressed by the covariation of co- and cross-polarized backscatter Γ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PP-PQ</sub> of the neighboring cells and assume it is indicative for the amount of a vegetation-only co-to-cross-polarized backscatter ratio μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PP-PQ</sub> . The ratio-based retrieval approach enables a relative (no absolute backscatter) estimation of the vegetation structure parameters which is more robust compared to retrievals with absolute terms. The application of the developed algorithm on global L-band Soil Moisture Active Passive (SMAP) radar data acquired from April to July 2015 indicates the potential and limitations of estimating these two parameters when no fully polarimetric data are available. A focus study on six different regions of interest, spanning land cover from barren land to tropical rainforest, shows a steady increase in orientation distribution toward randomly oriented volumes and a continuous decrease in shape arriving at dipoles for tropical vegetation. A comparison with independent data sets of vegetation height and above-ground biomass confirms this consistent and meaningful retrieval of A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> and ψ. The retrieved shapes and orientation distributions represent the main vegetation elements matching the literature results from model-based decompositions of fully polarimetric L-band data at the SMAP spatial resolution. Based on our findings, A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> and ψ can be directly applied for parameterizing the vegetation scattering component of model-based polarimetric decompositions. This should facilitate decomposition into ground and vegetation scattering components and improve the retrieval of soil parameters (moisture and roughness) under vegetation.

Review of the Comprehensive SAR Approach to Identify Scattering Mechanisms of Radar Backscatter from Vegetated Terrain

In a field of polarimetric synthetic aperture radar (SAR) remote sensing, various kinds of polarimetric decomposition techniques have been proposed. However, poor validations prevent them from operational applications. A true composition ratio of scattering mechanisms within a radar backscatter plays a key role. To overcome the issue, a novel comprehensive SAR approach to accurately identify a contribution of each scattering mechanism has been introduced. This is based on multiparametric SAR observation combined with a numerical model simulation. In this article, a comprehensive SAR approach is concisely reviewed to accelerate the research in this field. First, popular model-based polarimetric decompositions are introduced and their limitations are shown. Then, a behavior of scattering mechanisms is analyzed by the discrete scatterer model with some results using real multiparametric SAR data. A comprehensive SAR approach must be essential to realize an operational use of polarimetric SAR data.

Sensitivity Analysis of Multifrequency MIMP SAR Data From Rice Paddies

The determination of the accurate composition ratio of scattering mechanisms (volume scattering, double-bounce scattering, and surface scattering) within a radar backscatter is essential to validate current polarimetric decomposition techniques. Multiincidence angle and multipolarimetric synthetic aperture radar (MIMP SAR) observations at the X- and L-bands were applied to rice paddies at late vegetative stage in Niigata City in Japan in 2014 and 2016, respectively. In this paper, multifrequency MIMP SAR analysis is introduced based on the observation results. The approach, combined with theoretical characterization of the data by a discrete scatterer model, showed that rice panicles affect the backscatter from rice paddies. Contrary to expectation, an effect of transmissivity by using different bands is not obvious. The similar level of copolarization (HH and VV) backscatter at X- and L-bands could be explained by the effective size of rice panicles. They are the most characteristic scatters in rice paddy field with respect to multiple frequency polarimetric sensing. In addition, HV shows a distinct sensitivity to the mean orientation angle and the size of panicles regardless of the wavelength. The mean orientation angle affects the polarimetric randomness under azimuthal symmetry, whereas the size of panicles directly affects the attenuation of the volume scattering from the grains. The multifrequency MIMP SAR analysis also indicated the importance of considering the backscatter and attenuation in the interpretation of the backscattering cross section from vegetated fields.

Characterization of L-Band MIMP SAR Data From Rice Paddies at Late Vegetative Stage

Insufficient validation for polarimetric decomposition techniques has led to its less perceived popularity for more than 20 years. The true composition ratio of scattering mechanisms within a radar backscatter should be essential to make polarimetric synthetic aperture radar (SAR) operational applications. To achieve this, a novel comprehensive approach to accurately identify the contribution of each scattering mechanism by a multi-incidence angle and multipolarimetric (MIMP) SAR observation combined with a theoretical model simulation is newly applied to L-band SAR data. Rice paddies in Niigata, Japan having a simple vegetation structure without topography were observed by Polarimetric and Interferometric Airborne SAR L-band 2, by gradually varying the flight path in terms of incidence angle. In addition to the MIMP SAR observation, a dominant scattering mechanism is reliably isolated through the theoretical characterization of the data by a discrete scatterer model. Avoiding unnecessary Bragg scattering effect caused by the methodically distributed rice paddies, the volume scattering from grains is identified as a dominant scattering mechanism over incidence angles. In addition, HH and VV are strongly affected by the double-bounce scattering between stalks and the ground surfaces at only small incidence angles, whereas the contribution of the double-bounce scattering for HV is not obvious. The results at the L-band will be compared with another MIMP SAR data at the X-band obtained for the same rice paddies in 2014 so that multifrequency MIMP SAR data analysis shall be conducted for our next step.

Theoretical Characterization of X-Band Multiincidence Angle and Multipolarimetric SAR Data From Rice Paddies at Late Vegetative Stage

Various polarimetric decomposition techniques have been proposed and demonstrated for more than 20 years. However, they still have never been operational applications because of insufficient validations. The true composition ratio of scattering mechanisms within a radar backscatter has to be known. To achieve this, a novel comprehensive approach to accurately identify the contribution of each scattering mechanism by a multiincidence angle and multipolarimetric (MIMP) synthetic aperture radar (SAR) observation combined with a theoretical model simulation is introduced. Rice paddies in Niigata City in Japan having a simple vegetation structure without topography were observed by X-band polarimetric and interferometric SAR 2 (Pi-SAR2), by gradually varying the flight path in terms of incidence angle. In addition to the MIMP SAR observation, a dominant scattering mechanism is reliably isolated through the theoretical characterization of the data by a discrete scatterer model. In the case of the rice paddies at a late vegetative stage, a dominant scattering on HH gradually varies from the double-bounce scattering to the volume scattering of rice grains in terms of incidence angle, whereas VV is affected by various volume scatterings of grains, leaves, and stems at the small, medium, and large incidence angles, respectively. HV is simply affected by the volume scattering of grains at the small incidence angle, and then it gradually switches to the volume scattering of the stalks. This brand new approach by the MIMP SAR observation with the theoretical modeling for this specific stage could take forward the polarimetric decomposition studies.

A Generalized Radar Backscattering Model Based on Wave Theory for Multilayer Multispecies Vegetation

A generalized radar scattering model based on wave theory is described. The model predicts polarimetric radar backscattering coefficients for structurally complex vegetation comprised of multiple species and layers. Compared to conventional two-layer crown-trunk models, modeling of actual forests has been improved substantially, allowing better understanding of microwave interaction with vegetation. The model generalizes an existing single-species discrete scatterer model and, by including scattering and propagation effects through judiciously defined vegetation layers, enables its application to an arbitrary number of species types. The scatterers within each layer are modeled as finite cylinders or disks having arbitrary size, density, and orientation, as in the predecessor model. The distorted Born approximation is used to represent the propagation through each layer, while scattering from each is modeled as a linear superposition of scattering from its respective random collection of scatterers. Interactions of waves within and between each layer and direct scattering from the ground are accounted for. Validation of the model is presented based on its application to 23 wooded savanna sites located in Queensland, Australia, and comparison with Advanced Land Observing Satellite (ALOS) Phased Arrayed L-band Synthetic Aperture Radar (PALSAR) and National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL) Airborne Synthetic Aperture Radar (AIRSAR) data. Results indicate good agreement between simulated and actual backscattering coefficients, particularly at HH and VV polarizations. More discrepancies are found at HV polarizations and can be explained by uncertainties in the knowledge of input parameters, such as inaccuracies in the surface model, surface roughness parameterization, and soil moisture.

Discrete Scatterer Model for Analyzing Microwave Characteristics of Corn Canopy

Discrete Scatterer Model for Analyzing Microwave Characteristics of Corn Canopy

Soil Moisture Retrieval Using Data Cube Representation of Radar Scattering

A time-series algorithm is proposed to retrieve surface (from surface down to 1m depth) soil moisture using the simulated radar data. The time-series approach uses co-polarized (V V and HH) backscattering coe-cient (ae 0 ) values. Temporal averaging is applied to reduce the radar measurement noise. To the extent that the surface roughness does not change within the time-series window, the reduction of the noise enables the retrieval of the roughness. With the roughness estimate, subsequently soil moisture is retrieved. The proposed retrieval is per- formed using 'data cubes'. The data cubes relate soil moisture and ae 0 , and are lookup tables with the dimensions of soil moisture, roughness, and vegetation water content (VWC). The cubes are generated by the flrst-order small perturbation model and the discrete scatterer model for the grass vegetation. A Monte-Carlo analysis demonstrates that the soil moisture may be retrieved within the error better than 0.06cm 3 /cm 3 up to about 3kg/m 2 VWC using six time- series records, although presently assuming that the radar model correctly describes the surface scattering processes.

Soil moisture inversion at L-band using a dual-polarization technique: A model-based sensitivity analysis

The inverse problem of estimating soil moisture from vegetated and non-vegetated terrain is investigated using a passive microwave technique. The radiometer response at L-band is modelled by the Peake's approach that involves the integration of bistatic scattering coefficients to calculate surface emissivity. For vegetated terrain, a discrete scatter model employing the distorted Born approximation is used to obtain bistatic scattering coefficients. For non-vegetated rough surface, the Kirchhoff 's rough surface approximation is used to calculate bistatic scattering coefficients. A series of vegetated and non-vegetated surfaces are simulated for this study by changing vegetation densities and ground roughness conditions. The forward model is simplified so that it can be inverted with a minimum of auxiliary information about the vegetation and the ground. An inversion procedure is set up such that the ratio of horizontal to vertical Fresnel reflectivity is expressed in terms of dual-polarized microwave brightness temperatures (available from the forward model or a radiometer). The reflectivity ratio expression is then solved to obtain soil moisture. In the case of weak vegetation such as soybean canopy, no information regarding vegetation is necessary in the inversion procedure because the difference between horizontal and vertical optical depth is assumed to be negligibly small at low to medium viewing angles. The consequence of this assumption on the soil moisture estimation from canopies of higher Leaf Area Index (LAI) is analysed. Similarly, in the case of non-vegetated rough terrain, inversion is carried out without information about rough surface because the rms surface roughness height cancels out in ratioing of the Fresnel reflectivity. To account for instrument and other errors in experimental data, a random noise is added to model data and the rms error in soil moisture inversion is calculated for vegetated and non-vegetated terrain. A comparison of the dual polarization with single (horizontal) polarization technique reveals that the dual polarization is a better technique for soil moisture estimation. The sensitivities and implications of a priori information are discussed in the context of developing a soil moisture estimation algorithm from satellites to be launched in the forthcoming space missions.

A discrete-scatterer model for ultrasonic images of rough surfaces

Automated analysis of ultrasonic images could be greatly improved with model-based Bayesian methods for image analysis. Such an approach would require an accurate probabilistic image model representing ultrasonic images in terms of the gross shape of underlying anatomical structure. Existing probabilistic models for ultrasonic image data do not adequately incorporate structure shape or system characteristics; thus, a substantially new approach is warranted. Toward that goal, we have developed models for the imaging system and rough surface with the following objectives: (1) accuracy in representation of basic image characteristics such as the texture and intensity, (2) a minimum of computational requirements, and (3) a form that is naturally extendable to an appropriate probabilistic image model. The imaging system was modeled as a linear system with a separable three-dimensional point-spread function with an envelope of Gaussian curves in each dimension. The rough surface was modeled as a collection of discrete scatterers placed on the continuum and parametrized by a surface roughness and scatterer concentration. Models were evaluated by a visual comparison of actual and simulated images of a cadaveric lumbar vertebra. The gross shape of the vertebral surface was estimated from computed tomography images of the vertebra, and simulated images were generated using the models and the gross surface shape. Actual images were registered with the surface and simulated images to within 2 mm. The similarity of the actual and simulated images was quite remarkable considering the simplicity of the models. Differences between the images were less than those between two simulated images separated by 0.4 mm or one-fifth the registration error. Further assessment of the models would require a statistical approach not yet available. The models do, however, provide the basis for the development of a computationally tractable probabilistic image model for image analysis. Such a model will provide the means for a statistical evaluation of the system and surface models.

A multi-gate time-of-flight technique for estimation of temperature distribution in heated tissue: theory and computer simulation

Non-invasive determination of temperature distribution in biological media is important in many heating-related studies, such as thermal treatment. In this paper, we present an in vitro ultrasound technique for estimation of temperature distribution in heated tissue. Our technique consists of two major steps: (1) using multiple time gates to track echo signals scattered from tissue regions at different depths; (2) estimating temperature distribution based on heating-induced changes of arrival times of echo signals scattered from the targeted tissue regions. We use the conventional cross-correlation approach to track echoes. For temperature estimation, we have developed an iterative method that takes into account the influences of thermal expansion and heating-induced change in the speed of sound on the time of flight. We have introduced a concept of thermal sensitivity of the time of flight and used it to derive a theoretical formula that relates the achievable accuracy on the estimation of tissue temperature to seven parameters. The seven parameters are tissue thermal sensitivity of the time of flight, signal-to-noise ratio, bandwidth and center frequency of the signal, degree of signal decorrelation induced by changes in tissue physical properties during tissue heating, and widths and spacing of the time gates. We tested our technique by computer simulation, using a random discrete scatterer model and temperature distribution data acquired in our laser heating experiments on prostate tissue of live dog. Simulation results showed that our technique could accurately estimate the temperature distribution in the heated tissue. Our technique is fast in terms of computation and could be used as a research tool for in vitro real-time monitoring of temperature distribution in tissue under hyperthermal heating.

Discrete scatter model for microwave radar and radiometer response to corn: comparison of theory and data

As part of the Multisensor Aircraft Campaign, MACHYDRO, two microwave sensors, NASA's Airborne Synthetic Aperture Radar (AIRSAR) and Pushbroom Microwave Radiometer (PBMR) collected data over the same corn fields during the summer of 1990. During these flights, measurements were made on the ground of soil moisture and plant parameters. In this paper the measured canopy and soil parameters are used in a discrete scatter model to predict the response of both sensors (radar and radiometer). A distorted Born approximation is used to compute the scattering coefficient for the corn canopy. The backscatter coefficient gives the radar response and the radiometer response is obtained by integrating the bistatic coefficient over all scattering angles above ground. The objective of this analysis is to test the model and, in particular, to determine how well a single set of plant parameters and single model can yield agreement with both the radar and radiometer measurements. The model values are in reasonably good agreement with the measurements at horizontal polarization and reflect observed changes in soil moisture. >

The effect of topography on radar scattering from vegetated areas

The ways in which radar scattering from vegetated areas is affected by the topography of the surface underneath the vegetation are discussed. It is shown, using a discrete scatterer model, that the dominant scattering mechanism may change drastically when the ground surface is tilted relative to the horizontal. For a horizontal ground surface, for example, the total scattering may be dominated by scattering off the tree trunks, followed by a reflection off the ground surface. For a relatively small tilt in the ground surface, the ground-trunk interaction term may be replaced by scattering from the branches alone as the dominant scattering mechanism. The effect of the topography is more pronounced for scattering by longer wavelengths, and the implications on algorithms designed to infer forest woody biomass and soil and vegetation moisture using polarimetric SAR data are discussed. The effect of the topography on the scattering behavior from forested areas is illustrated with images acquired by the NASA/JPL three-frequency polarimetric SAR over the Black Forest in Germany. >

Microwave backscattering from a layer of randomly oriented discs with application to scattering from vegetation

The backscattering coefficients of a layer of vegetation over a fiat ground using discrete scatter model is studied. The vegetation layer is assumed to consist of randomly oriented leaves. The leaves are modelled by fiat, circular, dielectric discs. The distorted Born procedure is used for computing the mean field in the layer region which is due to an obliquely incident plane wave. Thebackscattering coefficients are then calculated by employing single scattering theory. In performing the necessary averaging, leaves are assumed to have orientation statistics that are azimuthally symmetric with respect to the layer normal. Numerical results for the skin depth of the mean wave and the backscattering coefficients are obtained for vegetation layer which consist of leaves onlyin the Rayleigh and geometric optics regimes.

Bi-Dynamic Reverberation and Acoustic Field Reconstruction

A signal that is generated by a moving source is spatially encoded by both the angular dependent Doppler shift in frequency and the angular dependent beam patterns of the transmitter. This information is preserved in the resulting reverberation and it has been theorized [R. Halley, “An Application of the Analysis of Reverberation from a Remote Pinging Searchlight Sonar,” TM 262, Navy Electron. Lab., San Diego, Calif. (1957)] that it can be recovered by means of a spectral analysis of the reverberation that is collected by an arbitrarily positioned receiver. To investigate this theory a bi-dynamic model of reverberation has been developed that is based on the Poisson distributed discrete scatterer model of Faure, Olshevski, and Middleton. The correlation function of the reverberation field was developed for various cases and the corresponding time-dependent power spectra have been computed. Certain of these results have been compared with data that were collected at sea.