Compressed sensing for medical applications

点击翻译按钮获取中文摘要

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.