Active Sonar Projection Tomography Imaging For Target Detection

The ocean we observed is a magnificent tapestry of information-bearing signals of many kinds (such as the marine biological signals, the environment’s signals caused by physical and chemical phenomena in the ocean, and man-made signals during human’s activities).For target detection in the ocean, we are faced with targets of interference which is much stronger of intensity and more of number than desired target, however, we take the signal of interference as a part of signal of scene. As we know, the ocean is a waveguide environment of space and time evolving, so the scientific problem we are dealing with is inverse problem of underdetermined. For such a problem, we need to develop the searching-tracking approach which only considering signal of target to imaging-searching-tracking approach which considering both signal of target and signal of scene. And imaging which is the preprocessor play the role of analyzing the scene, in another word, is extracting high dimensional signal of scene from relatively low dimensional measurement signals. Therefore, imaging is to solve an inverse problem of underdetermined. This paper use the method of projection tomography to illuminate the scene of appropriate scale from some different angles and collect a set of projections at those angles, and form an image of the scene, finally detect the target in the scene.Image formation can be taken as extracting information from the signal of observation to image the scene, and is mathematically described as estimating a two-dimensional or three-dimensional function(ρ(x, y) or p(x, y, z)) of the scene when given a set of one-dimensional waveforms sm(t) that depend on the scene. So we can take image-formation as transforming signals’ space-time domain (wavefront-waveform) into image domain. In most cases, we are faced with estimating images from incomplete and noisy data, usually estimating high-dimensional sets of indistinguishable discrete pixels from the low-dimensional measured signals, so we can abstract imaging into solving an underdetermined inverse problem. The solutions of such an underdetermined inverse problem is not unique. However, from the point of view of uncertainty measure, We can get the optimum solution with the corresponding criterion of Estimation Theory derived from least squares and Information Theory derived from entropy.Imaging mainly includes delay-doppler imaging, diffraction imaging, optical imaging and tomography. We will discuss tomography in this paper. For all the imaging systems, the most useful mathematical tools are the Fourier transform, the ambiguity functions, and the projection-slice theorem. The imaging resolution we mainly considering includes delay-dopplerresolution of the waveform and spatial direction resolution of the array manifold. The delaycorresponds to the radial distance, and the doppler corresponds to the radial speed. we propose todesign time-bandwidth product waveform whose ambiguity function concentrated, and designlarge space-bandwidth product array manifold whose response vector concentrated. The mosttwo essential methods of imaging are coherent processing technology and noncoherentprocessing technology, corresponding to deconvolution imaging and tomography respectively,the former is a matched filter form, using coherent accumulation to extract information aboutimage. the latter is the focus of the this paper, which mainly using noncoherent accumulationgenerating by space diversity to obtain image information gain. Based on the tomographytheoretical analysis, we will find the most important mathematical principles of tomography areprojection-slice theorem and Radon transform. We also can describe deconvolution imaging andprojection tomography respectively as algebraic method and geometric method.This paper mainly aims at active sonar tomography of underwater scene, we will transmitpulse train towards the observed scene with a small size real array which is moving along apredetermined ideal path，and receive the echo of single pulse at the corresponding viewingangle, then we can calculate the projection of this angle. When given the set of projection at allthose viewing angles, we can combine those projections to an image of scene with methods oftomography. However,the moving real array usually deviate from the predetermined ideal pathin real case,for this reason, it is needed to do motion compensation; and it is need to dofocusing compensation so that the phase of transmitted signal can be corrected in the center ofthe observed scene.The situation discussed in this paper is: a chirp pulse train is transmitted by a small sizereal array which is moving along a predetermined ideal path, meanwhile, every single pluse ofthe chirp pluse train is transmitted and received at its own viewing angle, then we construct theimage of scene with method of tomography. There are two ways dealing with it:(1)To fully process each single pulse of chirp pulse train by computing a samplecross-ambiguity function on each single pulse, and take the sample cross-ambiguity function as aprojection, then combine those projections to construct a image of scene with methods oftomography. (2)In some case, when given the echo of a single chirp pulse at a viewing angle, we can getdechirped pulse and then generate a slice approximately at this angle. For whole chirp pulsetrain, we can get a sequence of slice, and combine the sequence of slice to construct a by themethods of tomography.As mentioned below, the research contents of the paper can be divided five parts: the firstpart is an overview of imaging system; the second part discusses the fundamental mathematicalprinciple of imaging; the third part introduces the reflection imaging and diffraction imaging; thefourth part researches the theory and method of projection tomography imaging, and proves itwith simulations; the fifth part analyses the experiment research of projection tomographyimaging, finally, processes the Mogan Lake experiment data related to projection tomographyimaging and makes analysis of the result.