Financial markets produce massive amounts of complex data from multiple agents, and analyzing these data is important for building an understanding of markets, their formation, and the influence of different trading strategies. I introduce a signal processing approach to deal with these complexities by applying background subtraction methods to high frequency financial data so as to extract significant market making behavior. In foreign exchange, for prices in a single currency pair from many sources, I model the market as a low-rank structure with an additive sparse component representing...