Compressed sensing for medical applications

从数据中提取信息是信息时代普遍存在的问题。压缩感知是一种信息理论范式，它处理所提供的数据（测量）信息不足的情况;这一事实用于从较少的测量中推断出潜在的信息。最近的一个例子是COVID-19检测，SARS-CoV-2在人群中的低流行率意味着个体检测几乎总是呈阴性，传达的信息很少。明智地混合样本，测试混合样本并推断原始病毒载量值，可以显著减少获得相同信息所需的测试次数。类似地，磁共振成像（MRI）和计算机断层扫描（CT）扫描基于许多测量，并非所有测量都需要精确的图像重建，因为它们不是特别丰富的信息（具有非随机结构）。在这两个例子中，压缩感知方法可以帮助减少获得所需信息所需的测量数量。然而，样本的混合和使用的推理方法是不平凡的，需要新的想法和方法。此外，各种实际和操作约束阻碍了压缩感测在许多应用中的使用。该提案旨在解决成像和测试具体应用中的一些关键挑战。采用压缩感知进行测试的关键挑战是病毒载量的可变性，估计潜在的信息稀疏性和未知的样本噪声水平;两者都影响结果的效率和准确性（例如，假阳性/假阴性率）。在成像应用中，主要的障碍是在放射科医生的操作限制下（对位置进行校正，评估是否需要额外扫描）对大图像进行压缩感知所花费的时间。我们旨在研究的基于期望传播的方法的核心是与图像大小相关的大型矩阵的逆。在这个项目中，我们将采用基于统计物理和贝叶斯推理方法来克服这些挑战。具体而言，对于成像应用，我们将开发基于概率消息传递方法的快速矩阵求逆的近似方法，使用具有降低维度的图案化矩阵结构的变分近似，块矩阵求逆以及采用帧间和帧内先验。在大规模测试中使用压缩感知将需要使用先进的贝叶斯估计技术和改进的消息传递方法;这些将依赖于迭代变量抽取，以便移除高负载值以促进较低的负载值。我们将使用真实的扫描和模拟测试结果，这是广泛可用的，对国家的最先进的方法，我们的方法的性能进行评估。我们还将与放射科医生和考试中心的从业人员联络，以确保新方法符合实际限制和优先事项。如果成功的话，新的方法可以部署在各种应用程序中。

Extracting information from data is a ubiquitous problem in the information age. Compressed sensing is an information theoretical paradigm that deals with scenarios where the data provided (measurements) is poor in information; this fact is used for inferring the underlying information from fewer measurements. A recent example is COVID-19 testing, where low-prevalence of SARS-CoV-2 in the population means that individual tests almost always return negative and convey little information. Mixing samples judiciously, testing the mixed samples and inferring the original viral-load values, allows for a significant reduction in the number of tests needed to obtain the same information. Similarly, Magnetic Resonance Imaging (MRI) and Computerised Tomography (CT) scans are based on many measurements, not all of them needed for accurate image reconstruction since they are not particularly information rich (having a non-random structure). In both examples, compressed sensing methodology can help reduce the number of measurements needed for obtaining the information sought.However, the mixing of samples and the inference methods used are nontrivial and require new ideas and approaches. Moreover, various practical and operational constraints hinder the use of compressed sensing in many applications. This proposal aims at addressing some of the key challenges in the specific applications of imaging and testing. Key challenges in employing compressed sensing for testing are the variability in viral loads, estimating the underlying information sparsity and the unknown sample noise level; both impact on the efficiency and accuracy of the results (e.g., false positive/false negative rates). In imaging applications, the main stumbling block is the time it takes to carry out compressed sensing on large images given the operational constraints of radiologists (make correction to positions, evaluate the need for additional scans). At the heart of the expectation-propagation-based approach we aim on studying, is an inversion of a large matrix that is linked to the size of the images. In this project we will employ statistical physics-based and Bayesian inference methods to overcome these challenges. Specifically, for imaging application we will develop approximate methods for fast matrix inversion based on probabilistic message passing approaches, variational approximations using patterned matrix structures with reduced dimensionality, block matrix inversion and by employing inter- and intra-frame priors. Using compressed sensing in mass testing will require the use of advanced Bayesian estimation techniques and improved message passing methods; these will rely on iterative variable decimation, such that high load values will be removed to facilitate lower load values. We will use real scans and simulated test results, which are widely available, for evaluating the performance of our methods against state-of-the-art approaches. We will also liaise with radiologists and test-centre practitioners to make sure the new methods comply with practical constrains and priorities. If successful, the new methodologies could be deployed in a variety of applications.