> He suddenly realized that he could tame the distributions in SPDEs using an approach modeled on the mathematical properties of “wavelets” — brief, heartbeatlike oscillations that encode information in JPEG and MP3 files.

Wavelets are not used in JPEG or MP3 files. They're used in JPEG 2000 and video codecs like Dirac, which have failed to outperform DCT-based codecs like JPEG and MP3 and h.264.

Most of this article flew over my head though.