3-D Fourier Transform Beamforming

Sonar and radar detection,optical imaging,medical diagnosis,radio astronomy,microscopy,diffraction crystallography,seismology,etc.,these like the formation of the problem,not just physical problems,but also signal processing problems."The environment we are facing is like a gorgeous tapestry,with a variety of signals that carry information," which is the scene.We use our own organs or sensors to collect and process these signals to form the scene(visual)image,which is the scene like the formation.It is from the air-time domain(wavefront-wave)to the transformation of the image domain,where the Fourier transform plays the core role.The formation can be further abstracted as an inverse problem inference.However,due to the existence of uncertainty,different solutions may lead to the same fruit,so the solution of the inverse problem is not unique,there is no "right" solution,and we are pursuing a certain sense of the “best” solution.The axiomatic approach to the inference of the inverse problem is based on the axiom of the metric,and we use an inaccurate discriminant function as the distance between the measure,the description of the estimate and the prior conjecture,and that the estimate that minimizes the discriminant function is the "good " estimate.Using a variety of common inaccurate discriminant functions,the final derived best estimator is to correlate the model with the data,that is,the matched filter.Matching,is to use the problem of fitting the problem to solve the inverse problem,the problem of physical knowledge in which to help forward modeling to obtain the role of copy.The matched filter is a spectral estimator.The Blackman-Tukey spectral estimation method can be regarded as a discrete Fourier transform of a received signal with a different window function,or a correlation with a windowed complex exponential sequence,that is,a matched filter,so that the matched filter is also a spectral estimator The Time and space are dual,the time signal processing in the matching filter to the space,that is,beamforming,also known as spatial matching filter.It will collect the spatial signal associated with the copy,the inner product,as the beamforming output.The beamformer estimates the distribution of energy on the spatial spectrum and,therefore,can also be called a spatial spectrum analyzer.When space is a waveguide,one of the important developments in beamforming is based on Matched Field Processing(MFP)or Matched Field Beamforming.Its basic idea is still copy-related filtering,but its tolerance for mismatch is poor,and when the number of elements when the number of copies,and data-related computing volume is also larger.At present,the way humans detect the ocean is mainly the use of acoustic signals,that is,sonar detection technology.The shallow sea environment can be approximated into a three-dimensional waveguide with horizon and horizon expansion.This paper mainly studies the detection and location of the target,and puts it into the formation of the image.The basic method is Fourier transform beamforming.In this paper,the beamfront beamforming in the free field is classified into one-dimensional Fourier transform beamforming;the time-delay Doppler filter is classified into two-dimensional Fourier transform beamforming;the three-dimensional matching field beamforming in the waveguide is Three-dimensional Fourier transform beamforming.Based on the idea of image formation and spatial spectrum estimation,a new three-dimensional Fourier transform beamforming method is proposed.Firstly,the array domain data vector is transformed into three-dimensional Fourier transform to have higher signal-to-noise ratio and sparse spatial spectral domain data vector,that is,to obtain the image of the spatial spectrum,and then beamforming in the spatial spectral domain to obtain the image in the scanning position parameter space.Compared with the conventional matching field beamforming,the method reduces the amount of resolution,but eliminates the blurring and reduces the computational burden.In order to obtain the spatial spectrum better by three-dimensional Fourier transform,we discuss a Helix matrix with analytic three-dimensional Fourier transform expression and rich spatial orientation.We can use this method to make the ambiguity.Finally,the simulation and experiment of the Fourier transform beamforming of Helix array in three-dimensional waveguide are carried out,and the theory is verified.