Metagenomics is the study of communities of microorganisms through their sampled DNA. One of the first steps in a metagenomic study is called taxonomic profiling: determining the identity and relative abundance of the microbes present. Typical, this is a computationally time-consuming task as traditional approaches rely on classifying each individual read of DNA out of sample of up to billions of reads. In this talk, I will present one aspect of my research concerned with increasing the performance of the taxonomic profiling step by utilizing ideas from compressive sensing: uniquely solving an underdetermined system of linear equations using l1 minimization. In the process, I will detail how this approach leads to new insight into more general sparse recovery paradigms. After assessing the performance of this approach on realistic data, I will discuss an ongoing extension of this work that accounts for organism similarity using a non-convex lq-quasinorm optimization procedure.