Incomplete Inverse Problems in Nondestructive Testing and Imaging with Penetrating Radiation

在科学和工程调查中，当可测量的迹象不足以或不完全可信时，就会遇到不完整的问题，从而能够确定所研究系统的状态。在放射成像中，这种不完整性通过专家判断和对被检查对象或对象的性质的了解来补偿，或者通过与先前或其他独立的指征进行比较来补偿。尽管这些措施通常是有效的，但它们有时会失败，过去几年在加拿大和其他地方报告的医学成像误诊就是明证。鉴于现有的计算能力，在内存和速度方面，以及数字成像的广泛使用，从数据质量、图像质量甚至诊断的可信度方面对这些图像进行数值分析并不是不可能的。这可以通过将专家知识作为具有一定影响的概率估计纳入其中，或通过将其他指标作为约束并利用以前的趋势来限制评估范围来实现。这项建议解决了工业、安全和核保障应用的原子/核辐射非破坏性计算机成像这一特定领域中的这些不完整问题。将解决(1)输入数据的质量、(2)图像重建过程和(3)产生的图像的质量的三个方面。将开发从一条战线反馈到另一条战线的方法。目标是受益于专家知识和其他可获得的信息，同时将这一过程从主观判断中解放出来。所开发的工艺随后可用于医学成像。

Incomplete problems are encountered in scientific and engineering investigations when available measurable indications are not sufficient, or are not fully credible, to enable the determination of the state of a studied system. In radiological imaging, such incompleteness is compensated for by expert judgement and knowledge of the nature of the examined object or subject, or by comparison to previous or other independent indications. Although such measures are often effective, they sometimes fail, as evident by the medical imaging misdiagnosis reported in Canada and elsewhere within the past few years. Given available computing power, in terms of memory and speed, and the wide use of digital imaging, it is not inconceivable to numerically analyze such images in terms of the quality of data, the quality of the image and even the credibility of diagnosis. This can be accomplished by incorporating expert knowledge as probabilistic estimates with a certain degree of influence, or by accommodating other indications as constraints and utilizing previous trends to confine the range of assessment. Information from such exercise can also be utilized as feedback to the imaging process itself to improve its quality.This proposal addresses these incomplete problems in the particular area of non-destructive computed imaging with atomic/nuclear radiation for industrial, security and nuclear safeguard applications. The three fronts of (1) the quality of input data, (2) the image reconstruction process and (3) the quality of the produced image will be tackled. Methods for feedback from one front to the other will be developed. The goal is to benefit from expert knowledge and other available information, while liberating the process from subjective judgement. The developed processes can subsequently be adopted in medical imaging.