Sharif Behzad, Kamalabadi Farzad
Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
IEEE Trans Image Process. 2008 Feb;17(2):155-66. doi: 10.1109/TIP.2007.914225.
Determination of optimal sensor configuration is an important issue in many remote imaging modalities, such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed suboptimal backward greedy algorithm is used. A statistical framework is developed which allows for inclusion of several widely used image constraints. Computational complexity of the proposed algorithm is discussed and a fast implementation is described. Furthermore, upper bounds on the sum of the squared error of the proposed algorithm are derived. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented, and two application examples are described. Five compelling optimality criteria are considered, and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives.
在许多远程成像模态中，如断层成像和干涉成像，确定最佳传感器配置是一个重要问题。本文定义了一种统计最优性准则，并在候选传感器位置空间中进行搜索，以确定在所有候选配置中优化该准则的配置。为了使搜索过程在计算上可行，使用了先前提出的次优反向贪婪算法的改进版本。开发了一个统计框架，该框架允许纳入几个广泛使用的图像约束。讨论了所提算法的计算复杂度并描述了一种快速实现方法。此外，还推导了所提算法平方误差和的上界。介绍了该方法与用于子集选择问题的确定性反向贪婪算法的联系，并描述了两个应用示例。考虑了五个引人注目的最优性准则，并通过针对断层成像场景的数值实验研究了它们的性能。在所有情况下，均验证了所提算法设计的配置比明智选择的替代方案表现更好。
