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Reduction of the grating lobes in sparse array holographic sonar by projection onto convex sets

This paper describes a newly proposed image reconstruction algorithm and experimental results of a 3-D acoustical holographic imaging system which has an array composed of sparsely distributed transducer elements. The new algorithm is based on the projection onto convex sets (POCS) method. The POCS method allows the addition of convex sets constrained by the a priori information to reduce ambiguity in the image reconstruction process. By several experiments, it is proved that the concept of the image reconstruction algorithm has the following improvements. (1) The artifacts caused by the grating lobes can be reduced under the condition where the interval length is much larger than the wavelength. (2) The storage of the entire inverse matrix of K the degradation matrix of the imaging system is not required because the new image reconstruction algorithm is based on localized projection procedures. (3) The noise instability caused by the lack of knowledge of the point spread function can be reduced.