Identification and lossy reconstruction in noisy databases

A noisy database system is studied in which the noisy versions of the underlying feature vectors are observed in both the enrollment and the query phases. The noisy observations are compressed before being stored in the database, and the user wishes both to identify the correct entry corresponding to the noisy query vector and to reconstruct the original feature vector within a desired distortion requirement. A fundamental capacity/storage/distortion tradeoff is identified for this system in the form of single-letter information theoretic expressions. The relation of this problem to the classical Wyner-Ziv rate-distortion problem is shown, where the noisy query vector acts as the correlated side information in the lossy reconstruction of the feature vector.