Recovering Latent Signals from a Mixture of Measurements Using a Gaussian Process Prior

Abstract

In sensing applications, sensors cannot always mea-sure the latent quantity of interest at the required resolution, some-times they can only acquire a blurred version of it due the sensor’stransfer function. To recover latent signals when only noisy mixedmeasurements of the signal are available, we propose the Gaussianprocess mixture of measurements (GPMM), which models thelatent signal as a Gaussian process (GP) and allows us to performBayesian inference on such signal conditional to a set of noisymixture of measurements. We describe how to train GPMM, thatis, to find the hyperparameters of the GP and the mixing weights,and how to perform inference on the latent signal under GPMM;additionally, we identify the solution to the underdetermined linearsystem resulting from a sensing application as a particular case ofGPMM. The proposed model is validated in the recovery of threesignals: A smooth synthetic signal, a real-world heart-rate timeseries and a step function, where GPMM outperformed the stan-dard GP in terms of estimation error, uncertainty representation,and recovery of the spectral content of the latent signal.