SAS image reconstruction using Fast Polar Back Projection: comparisons with Fast Factored Back Projection and Fourier-domain imaging

Abstract

Abstrucr -Fast Polar Back-Projection (FPBP) is a variant of the Fast-Factored Back-Projection (FFBP) algorithm, originally developed for ultra-wideband airborne Synthetic Aperture Radar (SAR), but since applied with success to Synthetic Aperture Sonar (SAS). The paper outlines the FPBP and FFBP algorithms, comparing computation time and memory requirements for the two methods. Processing time comparisons with a standard FFT-based method are also given. Since FFBP and FPBP are both approximation methods, computation time also depends on the preset approximation error, which particutarly affects azimuth sidelobe level. The paper provides an opportunity to review speed and accuracy estimates made in previous literature. However reduction in computation time is not the decisive advantage of these timedomain methods. The difference from the FFT-based methods lies in the flexibility with which non-linear platform trajectories, wide swaths, wide bandwidths, and multi-element sonar arrays can be handled. It is also straightforward to obtain a set of intermediate physical aperture images for autopositioning purposes. I. INTRODUCTIONOver the last few years, there has been growing interest in iterative time-domain algorithms for SAS and SAR image reconstruction. These are more tolerant of non-linear platform trajectories and multi-channel antenna confgurations than the more familiar FFT-based algorithms (Chirp Scale, Range-Doppler etc. [1,2,3]), and have been claimed to achieve comparable execution times [4,5,6], The Fast Factored Back-Projection (FFBP) algorithm has been utilized for some years, but References 4-6 are actually predated by Houston's paper [7] on fast iterative beamformhg. Houston wrote his paper with large physical sonar antennas in mind, but the approach becomes even more interesting when applied to synthetic aperture sonar or radar imaging, where we christen it "Fast Polar Back Projection" (FPBP). In tbis paper we describe the differences between the FFBP and FPBP algorhhms, and present performance benchmarks, compared with each other and with the Chq-Scale Algorithm (CSA), which claims to be the fastest of the FFT methods. We will also discuss other advantages of the time-domain methods. II. OUTLINE OF METHODS A Phase-cenfresBoth FFBP and FPBP are easiest to describe in terms of "phase-centres", although it is unnecessary to use the phase-centre approximation in the actual algorithms [ 6 ] .

Shallow water height mapping with interferometric synthetic aperture sonar

“…Each synthetic aperture image is processed independently following the normal steps for image generation ( Figure 5): pulse compression; synthetic aperture processing using known navigation data and auto-focus. The synthetic aperture images are formed using a back-projection algorithm ( [10]) that uses the available precise navigation data and a prior rough estimate of the bottom height to synthesize motion error free images ( [4,8,9,12]). The images are also submitted through an auto-focus step to reduce phase errors due to motion uncertainties and medium fluctuations.…”

An algebraic approach to synthetic aperture sonar image reconstruction

“…The sonar platform seldom dislocates through in a straight line, and so the sonar model must account for the irregular along-track sampling positions ( [7,12]). Therefore the polar coordinate model must be abandoned and a broader expression for the echo travel time must contain the estimated position of the transducers and a rough estimation of the bottom height (a flat bottom is enough for a first approximation):…”

Sub-band processing of synthetic aperture sonar data

“…Processing the signal trough this technique can be used to obtain directly a coarse final synthetic aperture sonar image, or used in an global contrast optimization auto-focus algorithm ( [3,4,7]) with several steps with increasingly smaller wavelengths. This enables faster convergence through the resulting smother cost function surfaces (less impact of local minima).…”