Effectiveness of spatially-variant apodization
23 Oct 1995-Vol. 1, pp 147-150
TL;DR: It is shown that spatially-variant apodization is a special version of the minimum variance spectral estimator (MVSE), and that it has limitations for reconstructing real-valued extended targets.
Abstract: Sidelobe artifact is a common problem in image reconstruction from finite-extent Fourier data. Conventional shift-invariant windows applied to the Fourier data, reduce sidelobe artifacts at the expense of worsened mainlobe resolution. Stankwitz et al. (1995) have suggested spatially-variant apodization (SVA) as a means of reducing the sidelobe artifacts, while preserving the mainlobe resolution. SVA adaptively selects windows from a set of raised-cosine weighting functions. The algorithm is heuristically motivated, and is known to be effective in synthetic aperture radar (SAR) imaging. However, this technique has received only limited analysis. In this paper, we formulate SVA as a spectral estimator, and show that SVA is a special version of the minimum variance spectral estimator (MVSE). We study the properties of SVA that are inherited from MVSE. Then, we consider the application of SVA to spectral estimation and Fourier reconstruction. Although SVA is effective in SAR, we show that it has limitations for reconstructing real-valued extended targets.
Citations
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Book•
01 Jan 2005
TL;DR: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra.
Abstract: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.
2,620 citations
Patent•
28 Feb 2002TL;DR: In this paper, a high-definition radar imaging system and method receives image data and adaptively processes the image the data to provide a high resolution image The imaging technique employs adaptive processing using a constrained minimum variance method to iteratively compute the high definition image The highdefinition image I is expressed in range and cross-range as I(r,c)=minωHRω, where ω is a weighting vector and R is a covariance matrix of the image data.
Abstract: A high-definition radar imaging system and method receives image data and adaptively processes the image the data to provide a high resolution image The imaging technique employs adaptive processing using a constrained minimum variance method to iteratively compute the high-definition image The high-definition image I is expressed in range and cross-range as I(r,c)=minωHRω, where ω is a weighting vector and R is a covariance matrix of the image data A solution for I(r,c) is approximated by i) forming Y=[x1 xK]T/{square root over (K)} where x1 xk are beamspace looks formed from image domain looks and with y1, y2, and y3 denoting the K×1 columns of Y; ii) computing r21=y2 Ty1 and r31=y3 Ty1, and b=r21y2+r31y3; computing γ as γ = min ( r 21 2 + r 31 2 b T b , β - 1 r 21 2 + r 31 2 ) ; and iii) computing I(r,c) as I(r,c)=∥y1−γb∥2
62 citations
13 May 1996
TL;DR: The authors presented a technique based on the super-spatially variant apodization (super SVA) algorithm that can interpolate the collected data to fill the gap formed by the missing data that introduces a new potential price/performance tradeoff for the system designer with specific resolution requirements.
Abstract: Synthetic aperture radar (SAR) is a coherent imaging process that requires an uninterrupted collection of Nyquist-sampled signal data. Corrupted or missing data in the collected aperture produces artifacts and reduces the achievable resolution. For the case of corrupted data due to an improperly functioning system component or an intentional interference signal, simply nulling the corrupted part of the aperture will often improve the utility of the resulting image. However, significant artifacts will likely remain as a result of the gap introduced when the bad data is removed. The authors presented a technique based on the super-spatially variant apodization (super SVA) algorithm [Stankwitz and Kosek 1995] that can interpolate the collected data to fill the gap formed by the missing data. Super-SVB was originally designed to extrapolate SAR signal data; however, it can also be used to interpolate across gaps in the data. This technique can be extended to effectively build a large aperture from a number of closely spaced, but non-abutting, e.g. sparse, apertures. This ability to fill sparse apertures introduces a new potential price/performance tradeoff for the system designer with specific resolution requirements.
58 citations
TL;DR: Spatially variant apodization is reformulated for use on synthetic aperture radar imagery with an arbitrary sampling rate, and effectively eliminates sidelobe artifacts with no loss of mainlobe resolution.
Abstract: Spatially variant apodization (SVA) is reformulated for use on synthetic aperture radar imagery with an arbitrary sampling rate. The algorithm is implemented as a spatially varying three-point finite impulse response filter, and constraints on the filter parameters are developed from physically motivated concepts. By varying the parameters of the filter, the sidelobe energy is reduced with no effective loss of resolution. The procedure produces an output comparable to that of the integer Nyquist version of SVA, and effectively eliminates sidelobe artifacts with no loss of mainlobe resolution.
55 citations
Cites background from "Effectiveness of spatially-variant ..."
...However, SVA has been shown to be an efficient spectral estimator, exhibiting a pseudolinearity (linear when acting on separated impulses) and high resolution capabilities [ 5 ]....
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TL;DR: It is shown that SVA is a version of minimum-variance spectral estimation (MVSE), and a complete development of the four types of two-dimensional SVA for image reconstruction from partial Fourier data is presented.
Abstract: Sidelobe artifacts are a common problem in image reconstruction from finite-extent Fourier data. Conventional shift-invariant windows reduce sidelobe artifacts only at the expense of worsened mainlobe resolution. Spatially variant apodization (SVA) was previously introduced as a means of reducing sidelobe artifacts, while preserving mainlobe resolution. Although the algorithm has been shown to be effective in synthetic aperture radar (SAR), it is heuristically motivated and it has received somewhat limited analysis. In this paper, we show that SVA is a version of minimum-variance spectral estimation (MVSE). We then present a complete development of the four types of two-dimensional SVA for image reconstruction from partial Fourier data. We provide simulation results for various real-valued and complex-valued targets and point out some of the limitations of SVA. Performance measures are presented to help further evaluate the effectiveness of SVA.
30 citations
Additional excerpts
...We show that SVA is a special case of MVSE that exploits the computational efficiency afforded by using an infinite set of raised-cosine windows [ 15 ]....
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References
More filters
01 Jan 1978
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
7,130 citations
01 Aug 1969
TL;DR: In this article, a high-resolution frequency-wavenumber power spectral density estimation method was proposed, which employs a wavenumber window whose shape changes and is a function of the wave height at which an estimate is obtained.
Abstract: The output of an array of sansors is considered to be a homogeneous random field. In this case there is a spectral representation for this field, similar to that for stationary random processes, which consists of a superposition of traveling waves. The frequency-wavenumber power spectral density provides the mean-square value for the amplitudes of these waves and is of considerable importance in the analysis of propagating waves by means of an array of sensors. The conventional method of frequency-wavenumber power spectral density estimation uses a fixed-wavenumber window and its resolution is determined essentially by the beam pattern of the array of sensors. A high-resolution method of estimation is introduced which employs a wavenumber window whose shape changes and is a function of the wavenumber at which an estimate is obtained. It is shown that the wavenumber resolution of this method is considerably better than that of the conventional method. Application of these results is given to seismic data obtained from the large aperture seismic array located in eastern Montana. In addition, the application of the high-resolution method to other areas, such as radar, sonar, and radio astronomy, is indicated.
5,415 citations
"Effectiveness of spatially-variant ..." refers methods in this paper
...The minimum variance spectral estimator was originally developed by Capon [ 5 ] for frequency-wavenumber analysis in seismic arrays....
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TL;DR: A class of nonlinear operators which significantly reduce sidelobe levels without degrading mainlobe resolution implementation is presented, via sequential nonlinear operations applied to complex-valued (undetected) SAR imagery.
Abstract: Synthetic aperture radar (SAR) imagery often requires sidelobe control, or apodization, via weighting of the frequency domain aperture. This is of particular importance when imaging scenes containing objects such as ships or buildings having very large radar cross sections. Sidelobe improvement using spectral weighting is invariably at the expense of mainlobe resolution presented here is a class of nonlinear operators which significantly reduce sidelobe levels without degrading mainlobe resolution implementation is via sequential nonlinear operations applied to complex-valued (undetected) SAR imagery. SAR imaging is used to motivate the concepts developed in this work. However, these nonlinear apodization techniques have potentially broad and far-ranging applications in antenna design, sonar, digital filtering etc., i.e., whenever data can be represented as the Fourier transform of a finite-aperture signal. >
240 citations
"Effectiveness of spatially-variant ..." refers background or methods in this paper
...The extension of 1D SVA to the 2D application is discussed in [ 2 ]....
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...Stankwitz et a1.[ 2 ] have suggested spatially-variant apodization (SVA) for sidelobe control in SAR image processing....
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...Spatially-variant apodization, developed in [ 2 ], is a windowing operation that can sometimes reduce sidelobe artifacts....
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...Although [ 2 ] speculates that SVA may be a good tool for general windowing scenarios, our work suggests that SVA is best suited for situations involving isolated point targets, or coherent imaging of extended targets, where the reflectivity is modeled as being complex with random phase, resulting in a speckled reconstruction....
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01 Jun 1984
TL;DR: It is shown that high-quality speckle reconstructions are possible so long as the phase of f is highly random and the quality of the reconstruction is insensitive to the location of the known Fourier data.
Abstract: Motivated by the ability of synthetic-aperture radar and related imaging systems to produce images of surprisingly high quality, we consider the problem of reconstructing the magnitude of a complex signal f from samples of the Fourier transform of f located in a small region offset from the origin. It is shown that high-quality speckle reconstructions are possible so long as the phase of f is highly random. In this case, the quality of the reconstruction is insensitive to the location of the known Fourier data, and edges at all orientations are reproduced equally well. A large number of computer examples are presented demonstrating these attributes. Methods for improving image quality are also briefly discussed.
110 citations
"Effectiveness of spatially-variant ..." refers background in this paper
...Modeling the target to have random phase is appropriate for coherent imaging of targets that are rough compared with the wavelength of the transmitted signal [ 6 ]....
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