The Achievable Performance of Convex Demixing
Abstract¶
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the constituent signals follow a generic incoherence model, this analysis leads to precise recovery guarantees. These results admit an attractive interpretation: each signal possesses an intrinsic degrees-of-freedom parameter, and demixing can succeed if and only if the dimension of the observation exceeds the total degrees of freedom present in the observation.
Summary¶
Generalizes convex demixing analysis to superimposed, undersampled, and noisy observations, emphasizing the achievable limits of convex programs under generic incoherence. The central takeaway is geometric: each structure contributes an intrinsic degrees-of-freedom term, and convex demixing succeeds essentially when the measurement dimension exceeds the sum of those terms, giving a precise benchmark for what convex separation can and cannot recover.