Instituto de Telecomunicações and Departamento de Engenharia Electrotécnica e de Computadores, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal.
IEEE Trans Image Process. 1998;7(6):868-82. doi: 10.1109/83.679433.
This paper formulates and proposes solutions to the problem of estimating/reconstructing the absolute (not simply modulo-2pi) phase of a complex random field from noisy observations of its real and imaginary parts. This problem is representative of a class of important imaging techniques such as interferometric synthetic aperture radar, optical interferometry, magnetic resonance imaging, and diffraction tomography. We follow a Bayesian approach; then, not only a probabilistic model of the observation mechanism, but also prior knowledge concerning the (phase) image to be reconstructed, are needed. We take as prior a nonsymmetrical half plane autoregressive (NSHP AR) Gauss-Markov random field (GMRF). Based on a reduced order state-space formulation of the (linear) NSHP AR model and on the (nonlinear) observation mechanism, a recursive stochastic nonlinear filter is derived, The corresponding estimates are compared with those obtained by the extended Kalman-Bucy filter, a classical linearizing approach to the same problem. A set of examples illustrate the effectiveness of the proposed approach.
本文针对从噪声观测的实部和虚部中估计/重建复随机场的绝对（而不仅仅是模-2π）相位的问题进行了公式化和解决方案的提出。这个问题代表了一类重要的成像技术，如干涉合成孔径雷达、光学干涉、磁共振成像和衍射层析成像。我们采用了贝叶斯方法；因此，不仅需要对观测机制进行概率建模，还需要对要重建的（相位）图像有先验知识。我们选择非对称半平面自回归（NSHP AR）高斯-马尔可夫随机场（GMRF）作为先验。基于（线性）NSHP AR 模型的降阶状态空间表示和（非线性）观测机制，推导出了一个递归随机非线性滤波器，将对应的估计值与通过扩展卡尔曼-布西滤波器（一种经典的线性化方法）得到的估计值进行了比较。一组示例说明了所提出方法的有效性。
