Continuous noise-based monitoring of seismic velocity changes provides insights into volcanic unrest, earthquake mechanisms and fluid injection in the subsurface. The standard monitoring approach relies on measuring traveltime changes of late coda arrivals between daily and reference noise cross-correlations, usually chosen as stacks of daily cross-correlations. The main assumption of this method is that the shape of the noise correlations does not change over time or, in other terms, that the ambient-noise sources are stationary through time. These conditions are not fulfilled when a strong episodic source of noise, such as a volcanic tremor, for example, perturbs the reconstructed Green's function. In this paper, we propose a general formulation for retrieving continuous time-series of noise-based seismic velocity changes without the requirement of any arbitrary reference cross-correlation function (CCF). Instead, we measure the changes between all possible pairs of daily cross-correlations and invert them using different smoothing parameters to obtain the final velocity change curve. We perform synthetic tests in order to establish a general framework for future applications of this technique. In particular, we study the reliability of velocity change measurements versus the stability of noise CCFs. We apply this approach to a complex data set of noise cross-correlations at Klyuchevskoy volcanic group (Kamchatka), hampered by loss of data and the presence of highly non-stationary seismic tremors.