Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2012 Mar;59(3):590-604. doi: 10.1109/TUFFC.2012.2233.
Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced-rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects do not have orthonormal eigenfunction decompositions. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced-rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yielded approximations of scattering objects that were sufficiently accurate to allow residual variations to be reconstructed in a single iteration. Calculated scattering from a lossy elliptical object with a random background, internal features, and white noise is used to evaluate the proposed methods. Local reconstruction yielded images with spatial resolution that is finer than a half wavelength of the center frequency and reproduces sound speed and attenuation slope with relative root-mean-square errors of 1.09% and 11.45%, respectively.
利用奇异值分解（SVD）形成散射算子的降秩表示，提出了用于非径向有耗物体的高效逆散射算法。这些算法扩展了特征函数方法，因为这些方法不适用于非径向有耗散射物体，因为这些物体的散射算子没有正交特征函数分解。还提出了一种通过从不同局部区域分离散射贡献来进行局部重建的方法。通过形成散射算子的降秩表示来隔离每个区域的散射，该降秩表示的域和范围空间由远场模式组成，其中再发射场集中在局部区域。还给出了用于估计散射物体边界、平均声速和平均衰减斜率的方法。这些方法得到的散射物体近似值足够准确，可以在单个迭代中重建剩余变化。使用带有随机背景、内部特征和白噪声的有耗椭圆形物体的计算散射来评估所提出的方法。局部重建产生的图像具有比中心频率的半波长更精细的空间分辨率，并以相对均方根误差分别为 1.09%和 11.45%再现声速和衰减斜率。
