Comparison of Iterative Deconvolution Algorithmsfor the Mapping of Acoustic Sources

Abstract

The DAMAS2 algorithm is compared with several other Fourier-based deconvolution approaches. One is the Richardson-Lucy method, which is widely used for the deconvolution of astronomical images. The second is a modified gradient-type NNLS approach, where spectral procedures are implemented to accelerate the computations. Both methods require a computational effort similar to the DAMAS2 algorithm. All three algorithms use an approximate shift invariant point-spread function. %do not take the variation of the %point-spread function into account. %They solve the deconvolution problem only approximately. Furthermore it is described how the DAMAS2 and the Fourier-based NNLS algorithms can be embedded in an outer iteration loop to take the variation of the point-spread function into account. The resulting methods have two nested iterations, which require much more numerical effort than a single DAMAS2 iteration loop. All methods are tested with synthetic data. At first an example with a simple linear array and a small opening angle is considered, where the variation of the point-spread function in the source region is negligible. In this test case the results of the DAMAS2, the modified gradient-type NNLS, and the Richardson-Lucy algorithm are compared. It is shown that these algorithms more or less introduce oscillations in the reconstructed source distribution. A second test case with a planar array and a large opening angle is presented, to demonstrate the influence of a strong variation of the point-spread function. It is shown that the approximate methods lead to distorted results, while the methods with nested iterations give a significantly better reconstruction of the source distribution.