Randomized multi-pulse time-of-flight mass spectrometry

Mass spectrometry is one of the primary methods for chemical analysis and serves as a fundamental tool in numerous scientific disciplines. In this paper we consider the design of time-of-flight mass spectrometers, which produce a stream of measurements which can be modeled by a convolution between the mass spectrum of interest and a specified pulsing pattern. Our goal is to reduce the total time necessary to analyze a sample to a given precision (or equivalently, given a fixed amount of time, to obtain a more precise estimate of the sample). We can do this by leveraging the structure that exists in typical mass spectra. In particular, since any given substance is usually composed of a relatively small number of distinct molecules, mass spectra tend to be relatively sparse. In this paper we perform an analysis of an idealized model of a time-of-flight mass spectrometer which uses a randomized pulsing pattern. Such an architecture has the potential to enable a new tradeoff between acquisition time and precision/dynamic range. We show that under certain natural conditions on the randomized scheme - namely, that the system does not pulse too often - this construction will lead to a system which satisfies certain desirable properties that are sufficient to ensure that sparse recovery is possible. In particular, we show that with high probability, the system will satisfy the conditions of a bipartite expander graph provided the pulsing rate is not too large. We then conclude with a range of simulations that support our theoretical analysis and demonstrate the practical viability of this approach.