Proceedings Article | 21 November 1995
KEYWORDS: Data processing, Matrices, Fourier transforms, Antennas, Matrix multiplication, Reconstruction algorithms, Fused deposition modeling, Modulation, Image resolution, Zoom lenses
The frequency domain approach of Scansar problems suffers, numerically speaking, from the constrained smallness of the unit of azimuth increment. This unit is equal to the displacement of the craft between two consecutive transmission times, whatever the burst length, the latter conditioning the resolution of the coherent reconstruction. Thus a large oversampling occurs. There are three main ways of action to save computational effort: (1) The simplest one is to go out of the frequency domain with a dimension reduced transform operating on a cheap manipulation of the full frequential product. (2) The second one is to build the frequential input from several transforms at a dimension close to the burst, thus taking advantage of the initial zero padding. (3) The third one is to modify the 'static' template pipe in order to avoid repetitive operations in the signal pipe. A simple situation will be met where this policy is immediate. A much more intricate case of application leads to a hybrid algorithm connected with the SPECAN approach. The difference between the hybrid algorithm and Specan rests in the strictly diagonal character of the initial transformation performed on the burst in the Specan case, contrary to a narrow band matrix multiplication for the more general hybrid approach. The main lines of conclusion of this study are that, assorted with carefully designed numerical procedures, the frequency domain approach for Scansar is convenient, mainly, for coherent processing of rather longs bursts. More particularly, it combines well with frequential azimuth multilook. In the case of too short bursts, it becomes weaker than direct algebraic manipulation, but it gives an easy way for preparation of the needed static transformation matrices. The comparison with SPECAN approach is less easy, as the nets of points locations for reconstruction do not match. Nevertheless, a static transformation generalizes the Specan concept to prescribed grid by approximations coming from the hybrid algorithm. That new way could be challenging. The important theoretical part of this paper is clarified by illustrative means and some quicklook alternatives discussed in the function of, among other things, the imaging scenario, the required resolution, and the bursts length.
