The Necessary And Sufficient Condition for Generalized Demixing
Provides a theoretical foundation for demixing problems, benefiting signal processing and machine learning practitioners.
This work provides a necessary and sufficient condition for the success of convex optimization-based generalized demixing, enabling probability estimation via the approximate kinematic formula.
Demixing is the problem of identifying multiple structured signals from a superimposed observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. We present a new solution to determine whether or not a specific convex optimization problem built for generalized demixing is successful. This solution will also bring about the possibility to estimate the probability of success by the approximate kinematic formula.