High-Resolution Acoustical Image Reconstruction Algorithm for Finite-Size Objects: The Cascade Form

Abstract

Backward propagation has been one of the most widely used algorithms for acoustical image reconstruction and it is known that the resolution of the resultant images is governed by Rayleigh-criterion. The quality of the image reconstruction can be significantly improved by utilizing additional constraints such as the finite spatial-frequency bandwidth of the resultant waveneld and the finite size of the source region.It has been shown that we can utilize the finite frequency bandwith information to improve resolution by wavefield extrapolation. Recently, a more advanced reconstruction algorithm is formulated by using both the finite bandwidth and source size information for super-resolution imaging. However, the construction of the linear matrix operator of this algorithm is not computationally efficient because the elements of the matrix can not be formulated in closed form.This paper introduces the formulation of the optimal image reconstruction algorithm in a cascade form. Both the finite frequency bandwidth and source size are utilized for resolution enhancement. The enhancement matrix operation consists of three independent matrix operators: one for wavefield extrapolation, one for backward propagation, and one for spatial frequency bandwidth extension. All these operators are formulated independently in closed form to be computationally efficient. The formulation can also be used to evaluate the performance and limitation of discrete acoustical imaging systems in terms of the computation and resolution with respect to data acquisition, aperture size, source size, and noise level.KeywordsSource DistributionSource SizeResolution EnhancementImage Reconstruction AlgorithmNyquist RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.