We present a study to address the reconstruction of synthetic aperture radar (SAR) images using machine learning. From previous work, we utilize a single, fully-connected layer to learn the sensing matrix of the forward scattering problem by using a set of reflectivites as the inputs and the SAR measurements as the outputs. Using this result, we estimate the reflectivity of the SAR measurements by applying the conjugate transpose of the learned sensing matrix to the SAR measurement data. Then we further improve the reconstructions of the reflectivity using convolutional layers. Employing a training set made up of 50,000 images of randomly placed point scatterers as the reflectivities, we simulate SAR measurement data using a physical model for the sensing matrix. We apply the learned sensing matrix to our SAR measurement data and use this estimate of the reflectivity as the inputs to the model, while the true reflectivities are the outputs. The model is trained to reconstruct images containing a single target. We find that the resulting reconstructions are sharper images than those from the initial estimate from applying the conjugate transpose of the learned sensing matrix. In particular, we find that the background noise is significantly decreased. In addition, we test this model on a different dataset with multiple targets as reflectivities. Similar to previous results, and with no additional training, the model applied to data with multiple targets also demonstrated improved reconstructions of reflectivities.
Nonimaging optics is described in the context of radiative transfer theory. The radiative transport equation reduces to a local equation, whose solution can be expressed using the Green’s function formalism. This yields a surface integral equation for the radiance, which can be useful for analytical and numerical calculations.
We present a study that uses machine learning to solve the forward and inverse scattering problems for synthetic aperture radar (SAR). Using a training set of known reflectivities as inputs and the resulting SAR measurements as outputs, the machine learning method produces an approximation for the sensing matrix of the forward scattering problem. Conversely, employing that same training set but with the SAR measurements used as inputs and the reflectivities as outputs, the machine learning method produces an approximate inverse of the sensing matrix. This learned approximate inverse mapping allows us to solve the inverse scattering problem as it maps SAR measurements to an estimate of the reflectivity. To interpret these results, we restrict our attention to a neural network arranged as a single, fully-connected layer. By doing so, we are able to interpret and evaluate the mappings produced by machine learning in addition to the results of those mappings. Employing a training set made up of 50,000 of the CIFAR-10 dataset as the reflectivities, we simulate SAR measurements using a physical model for the sensing matrix. With this training set of reflectivities and corresponding SAR measurements, we find that the results of machine learning accurately approximate the sensing matrix and provide a better answer to the inverse scattering problem than the standard SAR inversion formula. We also test the performance of the proposed methodology on a dataset with high resolution images while training with a lower resolution data set. The results are very promising showing again a superior performance for the learned approximate inverse mapping.
We present a technique for determining the scattering coefficient of epithelial tissue from diffuse reflectance measurements due to an obliquely incident Gaussian beam. This method applies the convolution form of the diffuse reflectance as determined by the corrected diffusion approximation.
We study theoretically light backscattered by tissues using the radiative transport equation. In particular we consider a two-layered medium in which a finite slab is situated on top of a half space. We solve the one-dimensional problem in which a plane wave is incident normally on the top layer and is the only source of light. The solution to this problem is obtained formally by imposing continuity between the solutions for the upper and lower layers. However, we are interested solely in probing the top layer. Assuming that the optical properties in the lower layer are known, we remove it from the problem yielding a finite slab problem by prescribing an alternate boundary condition. This boundary condition is derived using the theory of Green's functions and is exact. Hence, one needs only to solve the transport equation in a finite slab using this alternate boundary condition. We derive an asymptotic solution for the case when the slab is optically thin. We extend these results to the three-dimensional problem using Fourier transforms. These results are validated by comparisons with numerical solutions for the entire two-layered problem.
We review the theory of the radiative transport equation governing the radiance in a random medium. Using symmetry and orthogonal properties of plane wave solutions, we can compute readily the Green's function for a uniform medium. We use this Green's function to develop a general theory for inhomogeneous media analogous to scattering theory for classical wave propagation.
We review the basic theory for the radiative transport equation governing light propagation in biological tissues. The Green's function is the fundamental solution to the transport equation from which all other solutions can be computed. We compute the Green's function as an analytical expansion in plane wave modes. We calculate these plane wave modes numerically using the discrete ordinate method. We use the Green's function to compute the point spread function in a half space composed of a uniform scattering and absorbing medium.
To examine the phenomenon of polarization memory, we examine time resolved backscattering of circularly polarized plane waves normally incident on a slab containing a random distribution of latex spheres in water. For large spheres polarization memory occurs a short time after first order scattering and before depolarization. It is the result of successive near forward scattering events that maintain the incident wave's helicity. For moderately large scatterers, it exhibits a simple dependence on the anisotropy factor. For larger spheres or those with higher refractive indices, it also depends on complicated angular and polarization characteristics of backscattering given by Mie theory.
Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward peaked scattering that the Fokker-Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the Fokker-Planck equation by Leakeas and Larsen provides an even better approximation and is also easier to solve. We demonstrate the accuracy of these two approximations by solving the problem of reflection and transmission of a plane wave normally incident on a slab composed of a uniform scattering medium.
We examine optical beam propagation and scattering in random media using three equations: radiative transfer, Fokker-Planck and Leakeas-Larsen. The Fokker-Planck equation gives a good approximation to the radiative transfer equation for foward peaked scattering phase functions. The Leakeas-Larsen equation gives an even better approximation. The solutions for all three of these equations can be represented as expansions in plane wave modes. Using these plane wave modes, we can compute solutions to these equations in a stable and efficient way.
Using radiative transfer, we investigate linear and circular polarized light normally impinging a plane-parallel medium containing a random distribution of identically sized latex spheres in water. The focus of this study is to understand fundamental properties of polarized light scattering. In particular, we analyze backscattered and transmitted flux responses computed form direct numerical simulations. Form these numerical computations, we observe that circular polarized light depolarizes at a slower rate than linear polarized light. In addition, circular polarized light shows a more noticeable dependence on the size of the scatterers than linear polarized light. Furthermore, the helicity flip observed in circular polarized backscattered light is a fundamental phenomenon manifested by low order scattering.
In this paper we present a theoretical study of focused beam wave pulse propagation and diffusion in highly scattering discrete random media. By using Wigner distributions, we calculate an explicit closed-form expression for the reduced intensity of focused beam waves. From this analysis, we find that the extent to which the reduced intensity focuses depends upon the attenuation it experiences from scattering and absorption. We then solve the diffusion equation for continuous wave sources and delta function input pulses to examine the spatial and temporal spreading of beam wave pulses. Through numerical approximations to the obtained solutions, we find that focusing effects of the diffuse intensity are negligible. Finally, we compare these results to those of collimated beam waves and pulsed plane waves. Through these comparisons, we determine that the spatial spreading of focused beams is similar to that of collimated beams, and the temporal spreading of the focused beam wave pulse is similar to that of plane wave pulses.
In this paper we present a theoretical study of focused beam wave pulse propagation and diffusion in highly scattering discrete random media. By using Wigner distributions, we calculate an explicit closed-form expression for the reduced intensity of focused beam waves. From this analysis, we find that the extent to which the reduced intensity focuses depends upon the attenuation it experiences from scattering and absorption. We then solve the diffusion equation for continuous wave sources and delta function input pulses to examine the spatial and temporal spreading of beam wave pulses. Through numerical approximations to the obtained solutions, we find that focusing effects of the diffuse intensity are negligible. Finally, we compare these results to those of collimated beam waves and pulsed plane waves. Through these comparisons, we determine that the spatial spreading of focused beams is similar to that of collimated beams, and the temporal spreading of the focused beam wave pulse is similar to that of plane wave pulses.
In this paper, we examine numerical solutions of the two- frequency radiative transfer equation to study pulse propagation through discrete random media. Specifically, we examine the plane-parallel problem using the Henyey- Greenstein phase function for scalar problems and Mie scattering for polarimetric problems. Since standard methods such as the discrete ordinate method and the finite element method are not numerically stable for polarimetric problems at large optical depths, we introduce a Chebyshev spectral method to solve these problems. Then, we examine a few examples of optical pulses in fog layers and millimeter wave pluses in rain layers, and compare our results to first- order scattering and diffusion approximations.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.