Title: | Advanced Array Imaging for Breast and Prostate Sonography |

Author: | Vaidyanathan, Ravi Shankar |

Abstract: | [Abstract from Thesis “Introduction .”] In conventional medical ultrasound such as B -mode imaging , the amplitude of the backscattered ultrasound pulse is used to image tissues along a fixed beam direction1 . This imaging technique works best in static organs , and it is difficult to image moving organs like the heart . The M -mode imaging technique is better for cardiac applications . For better image resolution , ultrasound tomography systems were developed in which ultrasound data were acquired by transducers placed in a circle around the object2 . This task of deriving the structure of the object from scattered radiation is known as the inverse scattering problem . The inverse scattering problem is known by several names like reflectivity tomography3 and diffraction tomography5 , 6 , 7 etc . Scattering refers to the effects on wave propagation due to an inhomogeneous medium . Since the inhomogenieties are unknown , the goal is to determine their properties – the spatial variation in density , compressibility , geometrical distribution etc . With the scattered wave field , determining the scatterer is called the inverse problem . As for the geometry of the scattering theory , the scatterer is assumed to be present in a homogeneous reference medium with known properties . Following the notations used in Lehman8 , the acoustic pressure , p , in this medium satisfies the Helmholtz equation (2 + k2 ) p (r ) = 0 where the pressure field is given by p (r ,t )=p0+p1 (r ,t ) The ambient pressure , p0 is constant . Since the scatterer is present in the reference homogeneous medium , the pressure field can be written as p0 (r ) = pinc (r ) + psc (r ) where pinc refers to the incident field and psc is the scattered field . In an ideal situation the incident pressure field is taken as a plane wave pinc (r ) = p0 eikz where k is the complex wave number which is given by k= ( /c ) (1 - iM ) where M is the compressional viscosity . Now , we are in a position to introduce the integral representations of the scattered field . In the region exterior to the scatterer , the pressure field is given by (2 + k2 ) p0 (r ) = 0 Introducing the Green’s function G (r – r’ ) = eik|r -r’| /|r -r’| that will satisfy the inhomogeneous impulse equation (2 + k2 ) G (r – r’ ) = -4 (r -r’ ) Using one of the most frequently used approximations , the Rayleigh -Born approximation we can modify equation (7 ) . At large distance the Green‟s function can be approximated by G (r – r’ ) ~ eikr /r e -ikr .r’ which holds true for k0r‟2 /r < <1 . A Fourier diffraction theorem based reconstruction technique using the Born approximation is derived in Radial Reflection Diffraction Tomography (RRDT ) 8 . Though my work is concerned with time -domain reconstruction techniques , I will discuss some existing frequency domain reconstruction techniques . |

URI: | http : / /hdl .handle .net /2152 .5 /208 |

Date: | 2010-05-14 |

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