Extensions of DAMAS and Benefits and Limitations of Deconvolution in Beamforming

Abstract

The DAMAS deconvolution algorithm represents a breakthrough in phased array imaging for aeroacoustics, potentially eliminating sidelobles and array resolution effects from beamform maps . DAMAS is an iterative non-negative least squares solver. The original algorithm is too slow and lacks an explicit regularization method to prevent noise amplification. Two extensions are proposed, DAMAS2 and DAMAS3. DAMAS2 provides a dramatic speedup of each iteration and adds regularization by a low pass filter. DAMAS3 also provides fast iterations, and additionally, reduces the required number of iterations. It uses a different regularization technique from DAMAS2, and is partially based on the Wiener filter. Both DAMAS2 and DAMAS3 restrict the point spread function to a translationally-invariant, convolutional, form. This is a common assumption in optics and radio astronomy, but may be a serious limitation in aeroacoustic beamforming. This limitation is addressed with a change of variables from (x,y,z) to a new set, (u,v,w). The concepts taken together, along with appropriate array design, may permit practical 3D beamforming in aeroacoustics.