Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar

Abstract

Convolution backprojection (CBP) image reconstruction has been proposed as a means of producing high-resolution synthetic-aperture radar (SAR) images by processing data directly in the polar recording format which is the conventional recording format for spotlight mode SAR. The CBP algorithm filters each projection as it is recorded and then backprojects the ensemble of filtered projections to create the final image in a pixel-by-pixel format. CBP reconstruction produces high-quality images by handling the recorded data directly in polar format. The CBP algorithm requires only 1-D interpolation along the filtered projections to determine the precise values that must be contributed to the backprojection summation from each projection. The algorithm is thus able to produce higher quality images by eliminating the inaccuracies of 2-D interpolation, as well as using all the data recorded in the spectral domain annular sector more effectively. The computational complexity of the CBP algorithm is O(N (3)).

A comparison of spotlight synthetic aperture radar image formation techniques

“…CBP uses the data on the polar grid directly to form a Cartesian image, and allegedly yields a higher quality image because all the Fourier data are used and two-dimensional interpolation is not required. This report describes in detail the implementation issues of the CBP algorithm, and more importantly addresses some of the claims made in [2]. In particular, we examine the conclusion that CBP provides better image quality than 2DFFT because "polar-to-Cartesian interpolation is computationally intensive and error prone due to interpolation inaccuracies" [2] and "polar-to-rectangular interpolation, which limits the achievable resolution, and therefore, the quality of the final image" [2].…”

“…This report describes in detail the implementation issues of the CBP algorithm, and more importantly addresses some of the claims made in [2]. In particular, we examine the conclusion that CBP provides better image quality than 2DFFT because "polar-to-Cartesian interpolation is computationally intensive and error prone due to interpolation inaccuracies" [2] and "polar-to-rectangular interpolation, which limits the achievable resolution, and therefore, the quality of the final image" [2]. We also dispute the assertion that CBP is better suited to parallel implementation, and show by way of examples that linear interpolation (and certainly nearest neighbor) is not acceptable under certain conditions.…”

“…A comparison using simulated SAR data is performed using more meaningful quality measures than that used in [2], and we show experimentally and theoretically that CBP does not yield higher quality images than the 2DFFT method. Then, we examine the parallel implementation of both image formation methods and show that the 2DFFT method is also inherently parallel.…”

“…2. More details of polarto-Cartesian interpolation are given in [4, 5, 61. We must address the contention in [2] that interpolation is " i n a c c~r a t e~~. If we are to believe the sampling theorem, which states that any continuous analog signal can be exactly reconstructed by samples of the signal taken at the Nyquist rate, then it should follow that correctly reconstructing the analog signal from its samples, and then resampling at the desired locations should be perfectly acceptable.…”

“…More recently, a method known as convolution backprojection (CBP) has been proposed for spotlight mode SAR image reconstruction [l], [2]. CBP uses the data on the polar grid directly to form a Cartesian image, and allegedly yields a higher quality image because all the Fourier data are used and two-dimensional interpolation is not required.…”