### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3aUW2. A minimum variance unbiased estimator for resolving blurred
beamformed images corrupted by signal-dependent speckle noise.

**Nicholas C. Makris
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*Naval Res. Lab., Washington, DC 20375
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A variety of methods currently exist for resolving the ambiguity and
blurring introduced by beamforming ocean acoustic line array measurements of
ambient noise [R. A Wagstaff, J. Acoust. Soc. Am. 63, 863--869 (1978)] and
reverberation [N. C. Makris, J. Acoust. Soc. Am. 94, 983--993 (1993)]. However,
these methods are not necessarily optimal because they assume that the measured
data are deterministic, whereas in actuality they are stochastic. An optimal
estimator for resolving such blurred beamformed images produces the minimum
variance possible and is unbiased in its output. Estimation theory is used to
derive such a minimum variance unbiased (MVU) estimator and to determine bounds
on the resolution of such blurred images. The fields measured by the array are
assumed to obey circular complex Gaussian random (CCGR) statistics, which have
previously been shown to describe a wide variety of ocean acoustic field
measurements from towed-array reverberation, to both horizontal and vertical
ambient noise. Given CCGR fields, the resulting beamformed images are corrupted
with signal-dependent noise known as speckle. Coherence theory for CCGR fields
is used to express the MVU estimator for resolving blurred images in terms of
the temporal coherence of the received fields and the measurement time.