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

Observations within sensing applications result from the convolution between the latent signal and the sensors's transfer function, therefore, a desired property of the sensor is to have a transfer function that is close to a Dirac delta function so that the latent signal can be recovered from the observations. We will model this convolution in a discrete manner to give rise to the representation of a sensing application described in Figure 1, where we model the observations as a (noisy) mixture of (again noisy) measurements and aim to recover the latent signal from the observations. Mixing of the latent signal's values stems from the inability of the sensor to measure the latent signal at the required resolution, this is due to low quality of the sensors that colour the observations which have to then be whiten in order to recover the latent process. Observations composed by mixtures of measurements are commonplace in sensing applications in different areas: in robot localization using radars or sonars [1], [2], in astronomical applications [3], and in super-resolution image recovery [4], to name but a few. A workaround to the problem of recovering a latent process from observations composed by mixtures of measurements is to define a set of sensing locations (i.e., a grid) and model F.T and G.R. and T.V. are with the Center for Mathematical Modeling (CMM), Universidad de Chile, and P.G is with the Computer Science Department and the Advanced Mining Technology Center, Universidad de Chile.