Sparse systems can be found many other places: genes that cause cancer, etc.
More importantly there’s a sparse representation for any signal. There is a sparse domain real world images, the wavelets domain. There’s a domain where audio signals tend to be sparse, the frequency/Fourier domain.
Solving these systems relies on a specific type of regularzation. The field of compressed sensing has risen from a 2006 Candes paper.
A first blush this looks like a lot of text not saying much. There is enough information there to cause me some interest, but some specific problems perhaps, or something we can actually do something about.