Sparse measurements, compressed sampling, and DNA microarrays

DNA microarrays comprising tens of thousands of probe spots are currently being employed to test multitude of targets in a single experiment. Typically, each microarray spot contains a large number of copies of a single probe designed to capture a single target, and hence collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Since only a small fraction of the total number of genes represented by the two samples is differentially expressed, a vast number of probe spots will not provide any useful information. To this end we consider an alternative design, the so-called compressed microarrays, wherein each spot is a composite of several different probes and the total number of spots is potentially much smaller than the number of targets being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. Moreover, we propose an algorithm which has far less computational complexity than the widely-used linear-programming-based methods, and can also recover signals with less sparsity.