  Scientific and commercial data is often incomplete. Recovery of the missing
information is an important pre-processing step in data analysis. Real-world
data can in many cases be represented as a superposition of two or more
different types of structures. For example, images may often be decomposed into
texture and cartoon-like components. When incomplete data comes from a
distribution well-represented as a mixture of different structures, a
sparsity-based method combining concepts from data completion and data
separation can successfully recover the missing data. This short note presents
a theoretical guarantee for success of the combined separation and completion
approach which generalizes proofs from the distinct problems.
