Incomplete Inverse Problems in Nondestructive Testing and Imaging with Penetrating Radiation

在科学和工程研究中，当现有的可测量指标不足以或不完全可信时，会遇到不完整的问题，以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检查对象或受检者性质的了解，或者通过与先前或其他独立指示进行比较来补偿。 虽然这些措施通常是有效的，但有时也会失败，过去几年在加拿大和其他地方报告的医疗成像误诊就是明证。 考虑到在存储器和速度方面的可用计算能力以及数字成像的广泛使用，在数据质量、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非不可想象。 这可以通过将专家知识作为具有一定程度影响的概率估计来实现，或者通过将其他指标作为约束条件来容纳，并利用以前的趋势来限制评估范围。 来自这种练习的信息也可以用作对成像过程本身的反馈以提高其质量。 该提案解决了在工业、安全和核保障应用中原子/核辐射的非破坏性计算机成像这一特定领域中的这些不完整问题。 将解决以下三个方面：（1）输入数据的质量，（2）图像重建过程和（3）所产生图像的质量。将制定从一个方面到另一个方面的反馈方法。其目标是利用专家知识和其他现有信息，同时使程序摆脱主观判断。 开发的过程可以随后在医学成像中采用。

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.