Bayesian signal extraction is a powerful technique used to extract meaningful signals from noisy time series data. In fact, the presence of random fluctuations and measurement errors can obscure the underlying patterns and make it difficult to identify and analyze the desired signal. In this paper we provide a Bayesian framework for modeling and separating background noise from the true signal in time series of calcium signals, the latter of which represents a fundamental task in the analysis of neuronal activity. We assume that the time series can be factorised into two processes; the first describes the evolution of the signal over time, while the second is a binary process that aims to determine whether the signal is present or not. We take advantage of recent research on dynamic sparse signals and adapt it to address this specific problem.