Alt uzay yöntemleri ile duvar arkası görüntüleme
Through wall imaging with subspace methods
Yazar: HÜSEYİN ÖNDER BEKTAŞ
Danışman: DOÇ. DR. ÖZGÜR ÖZDEMİR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Telekomünikasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2016
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Elektromanyetik görüntüleme = Electromagnetic imaging

Özet:
Gününmüz uygulamalarında yüksek çözünürlüklü radar görüntüleme önemli bir yere sahiptir. Klasik Fourier dönüşümü ile görüntüleme de ölçüm bir bant aralığında yapıldığından dolayı menzilde ki çözünürlük düşüktür. Çapraz menzilde ki çözünürlük ise anten açıklığına bağlıdır. Fourier ile yüksek çözünürlüklü görüntüleme yapılmak istenirse hem bant genişliğinin hem de anten açıklığının fazla olması gerekmektedir. Yapay olarak artırılabilen ve yapay açıklıklı radar olarak adlandırılan radar tipinde çapraz menzil çözünürlüğü önemli derecede artmaktadır. Şerit tarama tipi yapay açıklıklı radar da 2 boyutlu görüntü elde etmenin bir yolu her anten noktasında menzil profili denilen A tarama yapılarını bir araya getirmektedir. B tarama adı verilen iki boyutta radar görüntüsü bir boyutlu radar görüntülerinden oluşmaktadır. Bu durumda  görüntüleme de hiperbolik bozulmalar ortaya çıkmaktadır. İki boyutta yüksek çözünürlük ve doğrulukta görüntü elde etmek için algoritmaların iki boyutta gerçeklenmesi gerekmektedir.


Bu tez kapsamında görüntüleme yöntemlerinden ilk olarak duvar arkası görüntüleme de kullanılan çok yüksek çözünürlüklü bir alt uzay yöntemi olan MUSIC algoritması iki boyutta hem ham dataya hem de hüzme uzayında ki bir dataya uygulanmış ve mikrodalga görüntüleme yapılmaya çalışılmıştır. Zayıf saçıcı koşulu altında saçılan alan ile cisim fonksiyonu arasında bir Fourier dönüşümü ilişkisi vardır. Bu nedenden dolayı MUSIC algoritmasını ham ölçüm datasına uygulamak yerine hüzme uzayında ki dataya uygulanmış ve avantajları gösterilmiştir. Hüzme uzayında ki data hem zaman bölgesi hüzme şekillendirme hem de frekans dalgasayısı migrasyonu uygulanarak elde edilmiştir. Hem bilgisayar ortamında yapılan saçılan alan hesabıyla hem de deneysel olarak ölçülen radar datası ile yapılan gerçeklemeler tatmin edici sonuçlar vermiştir.

Görüntüleme yöntemlerinin ikinci kısmında  doğrudan örnekleme yöntemi incelenmiştir. Doğrudan örnekleme yönteminin en önemli avantajı tek bir verici anten altında saçılan alanın ölçülmesi  durumunda bile saçıcı cismin şeklini ve koordinatlarını doğru bir şekilde bulabilmektedir. Doğrudan örnekleme yöntemi herhangi bir optimizasyon gerektirmeyip sadece matris operatörleri kullanmaktadır. Bu basitlikten dolayı daha büyük adımlı görüntüleme algoritmalarında bir ön adım olarak kullanılabilmektedir. Bu amaçla multistatik ölçümde yapılan doğrudan örnekleme yöntemi aynı zamanda tek frekans ve çoklu frekans monostatik duruma da genişletilmiştir. Sayısal sonuçlar monostatik doğrudan örnekleme yönteminin efektif bir yöntem olduğunu göstermiştir.

Abstract:
High resolution radar imaging has an important position today's military and civilian applications. Through the wall radar imaging has increasing attention among the researcher because of the military and civilian applications. Behind the wall target detection and monitoring of suspected criminal can be given as an example of military applications. Rescue mission in the earthquake and searching survivor in the fire are two of the examples of civilian applications. These civilian application is vital for the human life under the emergency situation. Resolution is a important criterion for all these applications. Both range resolution and cross range resolution are expected to be as much as high.  Radar imaging using Fourier transform has lower range resolution because of limited bandwidth. Increasing the bandwidth require special hardware and this cause financially extra cost. Also wide bandwidth increase the integration time which is the total time during the measurement. Increasing the integration time is an essential problem for especially moving target behind the wall. Range of the target can be changed during the long integration time. Changing the range has an impact and cause the distortion in the radar image. Because of this reason, small integration time and limited bandwidth are more preferred. Cross range resolution depends on the antenna aperture. Both wide bandwidth and high antenna aperture are required to obtain high resolution radar image using Fourier transform. Antenna aperture can be increased synthetically by moving antenna along the path instead of increasing physically. This type of radar called synthetic  aperture radar or inverse synthetic  aperture radar, increase the cross-range resolution significantly. 


One dimensional radar image gives the information about the range of a target in each antenna position. Range profile can be obtained by using the time delay or phase information of measurement. Range is the proportional of the time delay or phase shift. This type of radar image is called A scan or range profile. One of the method to obtain two dimensional radar image using strip map synthetic  aperture radar is to gather range profile successively. This type of  radar image is called B scan which consist of one dimensional radar image. B scan is a two dimensional radar image which provide both range and cross range information the target. Single point target seems hyperbola in the B scan radar image. This type of phenomenon is called hyperbolic distortion. Even though B scan radar image can be obtain easily hyperbolic distortion arises because of the different travel time of the electromagnetic wave in the B scan. There are some algorithm in the literature to overcome this problem. SAR algorithm can be given as an example of this method. One of the method investigated in this thesis frequency wave number migration is one of the solution of avoiding hyperbolic distortion. This increase the computational cost and complexity. That is why the most convenient way to avoid the hyperbolic distortion in the radar image is to applied algorithm in the two dimension directly. 

In the first part of the imaging methods of this thesis, one of the high resolution subspace method multiple signal classification or MUSIC algorithm which is used for the through wall radar imaging is applied both element space data (row data) and beamspace data in two dimension. MUSIC algorithim is one of the spectral estimation technique for high resolution imaging algorithm which is applied synthetic  aperture radar and inverse synthetic  aperture radar imaging. MUSIC algorithm is based on the eigen value decomposition of correlation matrix or special operator is called time reversal operator. Correlation matrix or time reversal operator is divided into two orthonormal subspace signal and noise subspace depending on the eigen value. By looking at the projection onto noise subspace of each grid point in the search domain, unkown object can be determined. In the section three, imaging methods, MUSIC algorithm both mono static and multi static measurement are investigated individually. Inverse scattering problem deals with nonlinear problem. In the literature, some assumptions are done to linearize the problem. Born approximation and Rytov approximation are the most popular method to linearize the problem. According to the Born approximation, each target is assumed to be point target or relatively small compared to wavelength. Born approximation assume that there is no intersections between the point targets. Scattering field can be easily written as a summation of Green's function under the Born approximation. If the target and antennas are far away each other, Green's function can be written as an exponantial function. In that situation, there is a Fourier transform relation between the object function and scattering field under the Born approximation. Inverse scattering problem becomes finding suitable Fourier coefficient of the measurement or taking the inverse Fourier transform of measurement. This is why, MUSIC algorithm can be applied beamspace data instead of applying row data under the Born approximation. If the object function can be obtain by using the beamforming, Fourier transform of the object function is similar to row measurement data. Working in the beamspace provide some advantage in the imaging process. MUSIC algorithm simply based on the basic assumption of point targets or relatively small compare to the wavelength.  Non point targets or extended targets violate the point-target assumption. Even though MUSIC algorithm is based on the point target assumption, beamspace MUSIC do not require any assumption on target characteristics, in terms of type and size. Beamspace MUSIC is capable of finding both point targets and extended targets. Considering some challenges in the through wall radar, extended targets, small standoff distance and limited aperture and bandwidth. Beamspace MUSIC is capable for through wall imaging. To obtain beamspace data, different beamformer can be used. Each beamformer algorithm has own advantage and characteristics. It would be able to increase the signal to noise ratio, create a focused image or decrease the clutter or undesired interference signal. Each beamformer can be chosen different type of necessity. In this thesis, beamspace data is obtained both time domain delay and sum beamforming and frequency- wave number migration. Time domain delay and sum beamforming algorithm is applied to increase the signal to noise ratio of the measurement. Increasing the signal to noise ratio enable us to apply the algorithm in the highly noisy medium. Focused image is important for the resolution. The highly focused image is expected most of the through wall radar imaging applications. Focused image in two dimension can obtain by using frequency wave number migration. Beamspace MUSIC algorithim is investigated both case delay and sum beamforming and frequency wave number migration. Numerical verification of these algorihm are done both syntetic data and real through wall radar measurement. In the real through wall measurement, stepped frequency radar was used. Frequecny range is between the 3.75GHz and 13.5GHz. Human figure was used as a target behind the wall. Numerical results show the feasibility of the method.

In the second part of the imaging method, one of the simple algorithn for inverse scattering problem direct sampling method is investigated. Direct sampling method is based on the helmonthz equation.  The biggest advantage of the direct sampling method is that it is able to obtain shape and coordinate of the unknown target even if there is only one transmitter under the condition measurement is done far away from the target. Direct sampling method do not need any optimization and use only matrix operator. Direct sampling method require computing  only the dot product of scattering  field and fundamental solution of helmonthz equation directly. Because of the simplicity, it can be used as a initial step to estimate the inhomogeneous media for further process. Direct sampling method require multi static measurement. Mathmematical theory of direct sampling method is based on the multi static approach. In the last part of imaging methods, direct sampling method is extented to the monostatic case and multi frequency monostatic case. In the mono static case, fundamental solution of helmonthz equation can not used directly as a testing function. To overcome this problem we propose new testing function for mono static measurement set up. Simulation results give satisfactory result in the free space. Simulation results shows that single and multiple freqeucny direct sampling method for monostatic masuremenet is an effective method for inverse scattering problem.