Construct a probe and statistic pair enabling scene composition

Construct a probe and event-statistic pair for which the encoding function is an eigenfunction of the statistic and enables recovery of a dynamic scene composed of components with distinct temporal profiles and onset times.

Background

The inverse relations developed in the paper recover optical weights from event statistics when a single manufactured probe supplies the temporal variation and all pixels share one onset time. These conditions fail for a dynamic scene: different scene components may have different temporal profiles and arrival times, while the logarithmic photoreceptor makes the response to multiple components non-additive.

The authors identify a missing composition rule that would connect the statistics of individual scene components to the statistic of their superposition. Such a framework would need to handle onset diversity and preserve both component identity and temporal placement in a separable form. The paper suggests that an appropriate probe could make the event-statistic encoding function behave like an eigenfunction, but leaves the construction of such a probe-statistic pair unresolved.