Application of two-dimensional Nonuniform Fast Fourier Transform (2-D NUFFT) technique in synthetic aperture radiometer imaging
ABSTRACT This paper presents an accelerating Nonuniform Fast Fourier Transform (NUFFT) algorithm for imaging reconstruction of two-dimensional synthetic aperture radiometer. This algorithm relies on a mixture of the fast Gaussian gridding algorithm and the judicious use of the FFT on an oversampled grid. It is not limited for an equal spaced visibility function sampling, and has the advantage in storage compared with the traditional gridding method. It is also beneficial for the system optimization by testing a new antenna array configuration. The numerical simulation results indicate that the proposed algorithm is accurate and high-speed.
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ABSTRACT: Interferometric aperture synthesis is presented as an alternative to real aperture measurements of the Earth's brightness temperature from low Earth orbit. The signal-to-noise performance of a single interferometric measurement is considered, and the noise characteristics of the brightness temperature image produced from the interferometer measurements are discussed. The sampling requirements of the measurements and the resulting effects of the noise in the measurements on the image are described. The specific case of the electronically steered thinned array radiometer (ESTAR) currently under construction is examined. The ESTAR prototype is described in detail sufficient to permit a performance evaluation of its spatial and temperature resolution. Critical aspects of an extension of the ESTAR sensor to a larger spaceborne system are considered. Of particular important are the number and placement of antenna elements in the imaging arrayIEEE Transactions on Geoscience and Remote Sensing 10/1988; 26(5-26):597 - 611. DOI:10.1109/36.7685 · 3.51 Impact Factor
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ABSTRACT: We consider a simple approach for the fast evaluation of the Fourier transform of functions with singularities based on projecting such functions on a subspace of Multiresolution Analysis. We obtain an explicit approximation of the Fourier Transform of generalized functions and develop a fast algorithm based on its evaluation. In particular, we construct an algorithm for the Unequally Spaced Fast Fourier Transform and test its performance in one and two dimensions. The number of operations required by algorithms of this paper is O(N · logN + Np · (− log ϵ)) in one dimension and O(N2 · logN + Np · (− log ϵ)2) in two dimensions, where ϵ is the precision of computation, N is the number of computed frequencies and Np is the number of nodes. We also address the problem of using approximations of generalized functions for solving partial differential equation with singular coefficients or source terms.Applied and Computational Harmonic Analysis 10/1995; 2(4-2):363-381. DOI:10.1006/acha.1995.1026 · 3.00 Impact Factor
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ABSTRACT: In Earth observation programs there is a need of passive low frequency (L-band) measurements to monitor soil moisture and ocean salinity with high spatial resolution 10-20 km, a radiometric resolution of 1 K and a revisit time of 1-3 days. Compared to total power radiometers aperture synthesis interferometric radiometers are technologically attractive because of their reduced mass and hardware requirements. In this field it should be mentioned the one-dimensional (1D) linear interferometer ESTAR developed by NASA and MIRAS a two-dimensional (2D) Y-shaped interferometer currently under study by European Space Agency (ESA). Interferometer radiometers measure the correlation between pairs of nondirective antennas. Each complex correlation is a sample of the “visibility” function which, in the ideal case, is the spatial Fourier transform of the brightness temperature distribution. Since most receiver phase and amplitude errors can be hardware calibrated, Fourier based iterative inversion methods will be useful when antenna errors are small, their radiation voltage patterns are not too different, and mutual coupling is small. In order to minimize on-board hardware requirements-antennas, receivers and correlators-the choice of the interferometer array shape is of great importance since it determines the (u,v) sampling strategy and the minimum number of visibility samples required for a determined aliasing level. In this sense, Y-shaped and triangular-shaped arrays with equally spaced antennas are optimal. The main contribution of this paper is a technique that allows the authors to process the visibility samples over the hexagonal sampling grids given by Y-shaped and triangular-shaped arrays with standard rectangular FFT routines. Since no interpolation processes are involved, the risk of induced artifacts in the recovered brightness temperature over the wide held of view required in Earth observation missions is minimized and signal to noise ratio (SNR) is preserved. Peer reviewedIEEE Transactions on Geoscience and Remote Sensing 01/1997; · 3.51 Impact Factor