Missing values imputation and image registration for genetics applications

In this thesis, we address several common scenarios of corrupted data in data and image processing pipelines. The first is in the setting of clustered data with missing values. We design an algorithm for imputing missing values using optimal recovery and derive an error bound for non-negative matrix factorization of the imputed data. Second, we consider missing values as erasure channels and show examples of using Fano's inequality to find lower bounds on missing values algorithms. Finally, we perform image registration of misaligned and noisy images using multiinformation and use fi nite rate of innovation sample to speed up registration while preserving optimality