Pooled testing methods using compressed sensing for increasing the throughput and reliability of tests for the detection of defective units in a population

A method for pooled sample testing for a target substance using compressed sensing, the method comprising:

• receiving a plurality of individual samples;
• determining a mixing matrix for a plurality of pooled sample mixtures to create by mixing portions of selected ones of the plurality of individual samples;
• determining an allocation matrix for the plurality of pooled samples, wherein the allocation matrix allocations portions of each of the plurality of pooled samples for each test;
• performing mixing to create the plurality of pooled sample mixtures based on the mixing matrix and the allocation matrix;
• performing quantitative tests on the plurality of pooled sample mixtures so as to estimate an amount of the target substance contained within each of the plurality of pooled sample mixtures;
• and
• decoding results of the quantitative tests on the plurality of the pooled sample mixtures using the mixing matrix and the allocation matrix to determine quantitative estimates of amount of the target substance in each of the plurality of individual samples.