Mikrodalga difraksiyon tomografisi için yeni bir paralel işleme algoritması
A New parallel processing algorithm for microwave diffraction tomography
- Tez No: 39271
- Danışmanlar: PROF.DR. BİNGÖL YAZGAN
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 79
Özet
ÖZET Fiziksel özellikleri ve şekli bilinmeyen bir cismin, çeşitli uzaktan ölçme tekniklerinden yararlanılarak, bilinmeyen parametrelerinin hesaplanmaya çalışılması veya bir tahmininin elde edilmesi, yaygın bir araştırma ve inceleme alanı oluşturmaktadır. Doğrudan ölçme yöntemlerinin kullanılamadığı durumlar için, cismin bilinmeyen özelliklerinin belirlenmesinde, elektromagnetik veya akustik dalgalar kullanılarak tanımlanan ters saçılma yöntemleri günümüzde sıkça karşımıza çıkmaktadır. Mikrodalga difraksiyon tomografisinde, problemin çözümü için uygulanan yöntemlerden birisi olan Fourier difraksiyon teoremi, bazı yaklaşımlar altında zayıf saçıcı cisimler için yeterli sonuçlar vermesine karşılık, kuvvetli saçıcı cisimler için başarısız kalmaktadır. Bu durumda faklı ters saçılma algoritmaları ile çözümün elde edilmesi gerekir. Bu çalışmada, uzay domeninde moment yöntemi kullanan algoritmalara paralel işleme tekniği uygulanarak, görüntü oluşturmak ' amacı ile yeni bir algoritma geliştirilmiştir. Tezin birinci bölümünde dielektrik silindirik bir cisimden saçılan alanların analitik ifadesi verilmiştir. İkinci bölümde moment yöntemi ile bir ters saçılma algoritması verilmiş ve bu algoritmada deterministik ve iteratif çözümlerin kullanılması incelenmiştir. Üçüncü bölümde, önerilen paralel işleme yöntemi tanıtılmış ve deterministik çözümü kullanan ters saçılma algoritması bu yönteme uygulanarak yeni bir çözüm yolu ortaya konmuştur. Dördüncü bölümde, verilen yeni algoritmanın mikrodalga difraksiyon tomografisine uygulanması, çeşitli örnekler üzerinde incelenmiştir. Paralel işleme yönteminin kullanılması, ters saçılma algoritmasına oldukça önemli bir etkinlik ve hız kazandırmıştır. Bu yöntemin kullanılması ile bilinmeyen sayısının fazla olduğu durumlarda ortaya çıkan işlem karmaşası basitleştirilmiş ve hatalar azaltılmıştır. Böylece yüksek resolüsyonlu görüntülerin elde edilmesi sağlanmıştır.
Özet (Çeviri)
SUMMARY A NEW PARALLEL PROCESSING ALGORITHM FOR MICROWAVE DIFFRACTION TOMOGRAPHY The penetration ability of microwaves into various materials gives active microwave imaging a large potential for applications in many disciplines such as medicine, geophysics, and non-destructive testing. This fairly recent imaging technique is aimed at obtaining some information about the inside of an object exposed to incident microwave radiation from external scattered field measurement. During the last decade much attention has been paid to the development of reconstruction algorithms based on diffraction tomography. Tomography refers to cross-sectional imaging of an object from either transmission or reflection data. In the past, several algorithms based on the Fourier diffraction projection theorem were developed for electromagnetic diffraction tomography [1], Such algorithms are useful only if the object inhomogeneities are very small. In such a case two types of approximations, called the Born and the Rytov, are valid. However, they usually fail when applied to strong scatterers. In recent years, other techniques have been developed to image the strong scatterers in a simple way [9], [11]. In this thesis, an algorithm based on the inversion of the integral electromagnetic scattering equation is presented. The moment method is utilized to generate a matrix equation relating the scattered field values at discrete points located in the vicinity of the object. Hence, the unknown discrete permittivity distribution can then be determined by one matrix inversion and simple matrix operations such as additions and multiplications. The matrix solution can be carried out by either a direct (exact) matrix-inversion method or an indirect (iterative) method. Solution of the problem using the direct inversion of the matrix described in moment method fails when the number of unknowns increases. Instead of finding a solution by directly inverting the matrix, an adaptive prediction method can be given to find an estimate of the inverse matrix. The basic aim of this thesis is to produce a fast, simple method for solving the microwave imaging problem. For this reason, we present a new algorithm based on parallel processing techniques. The matrix described by the reconstruction algorithm is partitioned into submatrices and, the matrix-inversion method is applied to each submatrix independently. The new parallel processing architecture involves a number of stages. Each stage is designed in terms of its input vector and the desired output vectors. At the output of each stage, there is an error detection scheme. Each stage is essentially - VI -independent of the other stages in the sense that each stage does not receive its input directly from the previous stage. The new- algorithm has many desirable properties such as decreasing system complexity, determining the number of stages needed in each application, avoiding local minima, reducing the computing time, and truly parallel architectures in which all stages are operating simultaneously without waiting for data from each other during testing. Let us assume that the object is illuminated either from one or more directions with diffracting energy such as microwaves, and scattered fields are measured by receiver arrays as shown in Fig. 1. To estimate a cross-sectional image of an object, it is necessary to find a linear solution to the wave equation and then to invert this relation between the object function and the scattered field. Diffraction tomography algorithms are derived from the following general equation for the wave propagation in an inhomogeneous medium [4]: l^^kl}u{r)--kl0(?)U(?) (1) where u[f) represents the scalar field and o[?) the object function; which depends on the object inhomogeneities. The constant k0 is the complex wavenumber, v* is the two-dimensional Laplace operator and 7 denotes the two-dimensional position vector. It is assumed that the incident field Ut has only a z component and it is not a function of z, where the z axis is taken to be parallel with the axis of the object. A simple choice for the object function 0, is given by d Jfl -',e Figure 1. Geometry of the scattering system. - VII0(?) = er(?)-l (2) where, er{?) is the relative dielectric constant at r. The object is assumed to have the same permeability as free-space (m-/*.). The total field at any position can be modeled as a superposition of the incident field, */.(?), and the scattered field, u,[r), as given by u{7)=ut{7) + us{?) (3) where the scattered field u,[r) is given by the integral [5], tf,(F)-*o/ 0{?)u{r)G{7,r)d2r' (4) in which S is the scatterer cross section, G(r,r-o, (23d) where 17! is the least-squares solution of (23a), x+ is the inverse matrix of X, o, is the output signal of SI and ei is the error vector of SI. For stage 2, the input vector matrix is Y, and the desired output vector is et. A similar derivation yields YV2=el (24a) J72-r*e, (24b) o2=YW2 (24c) 62 = 61-02 (24d) where y* is the inverse matrix of Y and o2 is the output signal of S2. This process can be continued to any number of stages. XIII -We can improve the results discussed above further by forward- backward training of stages. We use ö = Oı + e3 as our new desired signal to obtain Vt and l/2 once more. The new equations for the first stage- can be given as 17,-jrC (25a) ff,-Xl71 (25b) and for the second stage ff, = £5-ffI (25c) tfj-r'fff. + oj (26a) ö2~Yff2 (26b) ^2 = (^1 + o2)-ff2 (26c) where l?i and I72 are the new coefficients, 8\ and S2 are the new output signals and Si and Sa are the new error signals at the output of each stage. We also prove that ll«Mla < ||r,||* s l|e2||s in section 3. We can make further error reduction by forward- backward training in which the desired output of each stage is modified as the previous output plus the remaining error from the previously processed stage. The procedure described above can be generalized for any number of stages. This procedure can be applied to Eq. (9). We can get the measured scattered field vector as a desired output vector. X, Y, Z,... corresponds to submatrices of the Green matrix and Wi corresponds to subvectors of the unknown object function. Each part of the vector W which includes the object function can be calculated at each step of the parallel processing procedure. It is possible to reduce the squared error by applying the forward-backward technique. The matrix inversion procedure for each submatrix can be carried out independently at the same time. This method gives us a fast and efficient way to solve the imaging problem. Some experimental results obtained by the new algorithm are presented in section 4. In the experiments, we used different type of objects with arbitrary cross sections. The objects are reconstructed either from noisily or noiseless scattered fields. The results are computed for the various number of measurement points. The reconstructed objects were obtained from two-stage and four-stage parallel processing systems. - XIV -X-[x\ x\ x*mY r-[y\ y\ y1.]' D-[di d2 dmY V,-[a, a2 a,]' V2-[bx b2 bj X and Y are m* p matrices. Each row of X or Y represents an input vector to SI or S2 respectively. D is the desired output vector of length m. t/i and W2 are the unknown coefficient vectors of SI and S2 respectively. They are of length p. We can write the following equations for the first stage. XV i- D (23a) VX"X*D (23b) ox = XWx (23c) o,«Z>-o, (23d) where 17! is the least-squares solution of (23a), x+ is the inverse matrix of X, o, is the output signal of SI and ei is the error vector of SI. For stage 2, the input vector matrix is Y, and the desired output vector is et. A similar derivation yields YV2=el (24a) J72-r*e, (24b) o2=YW2 (24c) 62 = 61-02 (24d) where y* is the inverse matrix of Y and o2 is the output signal of S2. This process can be continued to any number of stages. XIII -We can improve the results discussed above further by forward- backward training of stages. We use ö = Oı + e3 as our new desired signal to obtain Vt and l/2 once more. The new equations for the first stage- can be given as 17,-jrC (25a) ff,-Xl71 (25b) and for the second stage ff, = £5-ffI (25c) tfj-r'fff. + oj (26a) ö2~Yff2 (26b) ^2 = (^1 + o2)-ff2 (26c) where l?i and I72 are the new coefficients, 8\ and S2 are the new output signals and Si and Sa are the new error signals at the output of each stage. We also prove that ll«Mla < ||r,||* s l|e2||s in section 3. We can make further error reduction by forward- backward training in which the desired output of each stage is modified as the previous output plus the remaining error from the previously processed stage. The procedure described above can be generalized for any number of stages. This procedure can be applied to Eq. (9). We can get the measured scattered field vector as a desired output vector. X, Y, Z,... corresponds to submatrices of the Green matrix and Wi corresponds to subvectors of the unknown object function. Each part of the vector W which includes the object function can be calculated at each step of the parallel processing procedure. It is possible to reduce the squared error by applying the forward-backward technique. The matrix inversion procedure for each submatrix can be carried out independently at the same time. This method gives us a fast and efficient way to solve the imaging problem. Some experimental results obtained by the new algorithm are presented in section 4. In the experiments, we used different type of objects with arbitrary cross sections. The objects are reconstructed either from noisily or noiseless scattered fields. The results are computed for the various number of measurement points. The reconstructed objects were obtained from two-stage and four-stage parallel processing systems. - XIV -
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