The achievable performance of convex demixing

TL;DR

This paper analyzes the limits of convex optimization methods for demixing structured signals from noisy, undersampled observations, providing precise recovery guarantees based on the signals' degrees of freedom.

Contribution

It introduces a general framework for demixing using convex optimization and establishes exact conditions for successful recovery based on signal incoherence and degrees of freedom.

Findings

Recovery succeeds if observation dimension exceeds total degrees of freedom.

Provides explicit recovery guarantees for signals following a generic incoherence model.

Offers an interpretation linking signal structure to demixing feasibility.

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.