Debiased LASSO Methods for Compressed Sensing Based Group Testing

This thesis looks at how to identify a small number of faulty items using far fewer tests than testing each item one by one. It improves upon a popular mathematical tool, the Lasso, which is fast but often gives biased results. First, a new way is introduced to remove this bias more efficiently, making the method faster and easier to use. Next, the thesis tackles a practical issue: test groups may be formed incorrectly in real situations. A new method, ODRLT, is developed to detect both faulty items and wrongly formed groups. Finally, techniques are introduced to correct such grouping errors on the fly using only the test results.