类梯度变分贝叶斯方法:在乳腺肿瘤微波成像检测中的应用

L. Gharsalli, B. Duchêne, A. Mohammad-Djafari, H. Ayasso
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引用次数: 1

摘要

本文用变分贝叶斯方法求解了一个非线性逆散射问题。目的是通过测量不同频率和不同光照下的散射场来检测乳腺肿瘤。这个反问题是已知的非线性和不适定的。因此,需要通过引入先验信息对其进行正则化。在这里,所寻求的对象的先验信息是,它是由分布在紧凑区域的有限已知数量的不同材料组成的。这是通过在贝叶斯框架中处理问题来解释的。然后,利用类梯度变分贝叶斯技术,用可分离律逼近真关节后验。后者适用于复值对比,并通过联合更新近似边缘的形状参数来计算后验估计量。在综合数据上重建了介电常数图和电导率图,结果表明重建质量好,收敛速度快于经典变分贝叶斯方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A gradient-like variational Bayesian approach: Application to microwave imaging for breast tumor detection
In this paper a nonlinear inverse scattering problem is solved by means of a variational Bayesian approach. The objective is to detect breast tumor from measurements of the scattered fields at different frequencies and for several illuminations. This inverse problem is known to be non linear and ill-posed. Thus, it needs to be regularized by introducing a priori information. Herein, prior information available on the sought object is that it is composed of a finite known number of different materials distributed in compact regions. It is accounted for by tackling the problem in a Bayesian framework. Then, the true joint posterior is approximated by a separable law by mean of a gradient-like variational Bayesian technique. The latter is adapted to complex valued contrast and used to compute the posterior estimators through a joint update of the shape parameters of the approximating marginals. Both permittivity and conductivity maps are reconstructed and the results obtained on synthetic data show a good reconstruction quality and a convergence faster than that of the classical variational Bayesian approach.
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