Mikrodalga difraksiyon tomografisi için yeni bir paralel işleme algoritması

Abstract

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.

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. - VII 0(?) = 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