This papers examines the problem of a local band-width recovery for non-stationary stochastic signals when the only available information is given in terms of level crossings. The use of multiple level crossings is a fundamental paradigm for the recently investigated event-based sampling approach. In fact, level crossings allows us to exploit local signal properties and to avoid unnecessarily fast sampling when the local signal intensity is low. The paper proposes the least-square based method for the local intensity estimation from level crossings for the class of signals being the time-warped version of the stationary and bandlimited Gaussian processes. This result is then related to the concept of the local mean bandwidth and finally to the local power bandwidth. The smooth convolution estimate of the local intensity is proposed and its positivity corrected version is introduced. The latter is achieved by the truncation argument and next by the method of alternating projections onto convex sets.
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