Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes.Kirscht, Martin, and Carsten Rinke. "3D Reconstruction of Buildings and Vegetation from Synthetic Aperture Radar (SAR) Images." MVA. 1998. SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture (the size of the antenna). Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical (a large antenna) or synthetic (a moving antenna) – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer – therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.
To create a SAR image, successive pulses of radio waves are transmitted to "illuminate" a target scene, and the echo of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single beam-forming antenna, with wavelengths of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. Signal processing of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the synthetic antenna aperture and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna."Introduction to Airborne RADAR", G. W. Stimson, Chapter 1 (13 pp).
Motivation and applications
SAR is a form of remote sensing which has several notable merits:
SAR instruments can produce imagery during day or night as they produce their own illumination.Tomographic SAR. Gianfranco Fornaro. National Research Council (CNR). Institute for Electromagnetic Sensing of the Environment (IREA) Via Diocleziano, 328, I-80124 Napoli, ITALYSynthetic Aperture Radar Imaging Using Spectral Estimation Techniques. Shivakumar Ramakrishnan, Vincent Demarcus, Jerome Le Ny, Neal Patwari, Joel Gussy. University of Michigan. RADAR waves strongly penetrate many atmospheric phenomena, often allowing imaging irrespective of weather. Notably a region may be imaged even when covered by clouds. Despite the long RADAR wavelengths used and distance to the planet surface, SAR satellites can still produce high-resolution imagery by exploiting the synthetic aperture technique.Oliver, C. and Quegan, S. Understanding Synthetic Aperture Radar Images. Artech House, Boston, 1998. SAR systems produce coherent radiation allowing for techniques beyond straightforward imaging, such as polarimetry and interferometry.
SAR images have wide applications in both Earth observation as well as investigations of other planets. SAR is used to measure topography, map types of terrain and land use, observe the dynamics of glaciers, and image subsurface geological bodies. SAR is also used to monitor bodies of water by mapping ice cover, tracking icebergs, and detecting oil slicks. SAR is used in forestry to determine forest height, biomass, and the occurrence of deforestation. Differential interferometry is used in the monitoring of volcanoes and earthquakes. SAR is also applied for observing human-made infrastructure such as in the monitoring of armed conflicts and genocide, and the detection of structural deformation in bridges. Other phenomena commonly observed using SAR include flooding, urban growth, and military surveillance.
Basic principle
A synthetic-aperture radar is an imaging radar mounted on a moving platform. SAR is a Doppler technique. It is based on the fact that "radar reflections from discrete objects in a passing radar beam field each [have] a minute Doppler, or speed, shift relative to the antenna".Carl Wiley, working at Goodyear, Arizona, (which later became Goodyear Aerospace, and eventually Lockheed Martin Corporation) in 1951, suggested the principle that – because each object in the radar beam has a slightly different speed relative to the antenna – each object will have its own doppler shift. A precise frequency analysis of the radar reflections will thus allow the construction of a detailed image.
In order to realise this concept, electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different small positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width. That is the source of the term "synthetic aperture," giving it the property of an imaging radar. The range direction is perpendicular to the flight track and perpendicular to the azimuth direction, which is also known as the along-track direction because it is in line with the position of the object within the antenna's field of view.
The 3D processing is done in two stages. The azimuth and range direction are focused for the generation of 2D (azimuth-range) high-resolution images, after which a digital elevation model (DEM) is used to measure the phase differences between complex images, which is determined from different look angles to recover the height information. This height information, along with the azimuth-range coordinates provided by 2-D SAR focusing, gives the third dimension, which is the elevation. The first step requires only standard processing algorithms,G. Fornaro, G. Franceschetti, "SAR Interferometry", Chapter IV in G. Franceschetti, R. Lanari, Synthetic Aperture Radar Processing, CRC-PRESS, Boca Raton, Marzo 1999. for the second step, additional pre-processing such as image co-registration and phase calibration is used.
In addition, multiple baselines can be used to extend 3D imaging to the time dimension. 4D and multi-D SAR imaging allows imaging of complex scenarios, such as urban areas, and has improved performance with respect to classical interferometric techniques such as persistent scatterer interferometry (PSI).
Algorithm SAR algorithms model the scene as a set of point targets that do not interact with each other (the Born approximation).
While the details of various SAR algorithms differ, SAR processing in each case is the application of a matched filter to the raw data, for each pixel in the output image, where the matched filter coefficients are the response from a single isolated point target. In the early days of SAR processing, the raw data was recorded on film and the postprocessing by matched filter was implemented optically using lenses of conical, cylindrical and spherical shape. The Range-Doppler algorithm is an example of a more recent approach.
Existing spectral estimation approaches
Synthetic-aperture radar determines the 3D reflectivity from measured SAR data. It is basically a spectrum estimation, because for a specific cell of an image, the complex-value SAR measurements of the SAR image stack are a sampled version of the Fourier transform of reflectivity in elevation direction, but the Fourier transform is irregular.Xiaoxiang Zhu, "Spectral Estimation for Synthetic Aperture Radar Tomography", Earth Oriented Space Science and Technology – ESPACE, 19 September 2008. Thus the spectral estimation techniques are used to improve the resolution and reduce speckle compared to the results of conventional Fourier transform SAR imaging techniques.
Non-parametric methods
FFT
FFT (Fast Fourier Transform i.e., periodogram or matched filter) is one such method, which is used in the majority of the spectral estimation algorithms, and there are many fast algorithms for computing the multidimensional discrete Fourier transform. Computational Kronecker-core array algebra is a popular algorithm used as new variant of FFT algorithms for the processing in multidimensional synthetic-aperture radar (SAR) systems. This algorithm uses a study of theoretical properties of input/output data indexing sets and groups of permutations.
A branch of finite multi-dimensional linear algebra is used to identify similarities and differences among various FFT algorithm variants and to create new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set of factors, called functional primitives, which are individually identified with an underlying software/hardware computational design.
The FFT implementation is essentially a realization of the mapping of the mathematical framework through generation of the variants and executing matrix operations. The performance of this implementation may vary from machine to machine, and the objective is to identify on which machine it performs best.
Advantages
Additive group-theoretic properties of multidimensional input/output indexing sets are used for the mathematical formulations, therefore, it is easier to identify mapping between computing structures and mathematical expressions, thus, better than conventional methods. The language of CKA algebra helps the application developer in understanding which are the more computational efficient FFT variants thus reducing the computational effort and improve their implementation time.
Disadvantages FFT cannot separate sinusoids close in frequency. If the periodicity of the data does not match FFT, edge effects are seen.
Capon method The Capon spectral method, also called the minimum-variance method, is a multidimensional array-processing technique. It is a nonparametric covariance-based method, which uses an adaptive matched-filterbank approach and follows two main steps: Passing the data through a 2D bandpass filter with varying center frequencies (). Estimating the power at () for all of interest from the filtered data.
The adaptive Capon bandpass filter is designed to minimize the power of the filter output, as well as pass the frequencies () without any attenuation, i.e., to satisfy, for each (),
subject to
where R is the covariance matrix, is the complex conjugate transpose of the impulse response of the FIR filter, is the 2D Fourier vector, defined as , denotes Kronecker product.
Therefore, it passes a 2D sinusoid at a given frequency without distortion while minimizing the variance of the noise of the resulting image. The purpose is to compute the spectral estimate efficiently.
Spectral estimate is given as
where R is the covariance matrix, and is the 2D complex-conjugate transpose of the Fourier vector. The computation of this equation over all frequencies is time-consuming. It is seen that the forward–backward Capon estimator yields better estimation than the forward-only classical Capon approach. The main reason behind this is that while the forward–backward Capon uses both the forward and backward data vectors to obtain the estimate of the covariance matrix, the forward-only Capon uses only the forward data vectors to estimate the covariance matrix.
Advantages Capon can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the fast Fourier transform (FFT) method. Capon method can provide much better resolution.
Disadvantages