Privacy Preserving Deep Unrolling Methods and Its Application to Image Reconstruction

This paper introduces novel privacy-preserving deep unrolling techniques for recovering sparse signals, integrating privacy-preserving methodologies grounded in random unitary transformation. This approach facilitates data analysis and signal processing while safeguarding privacy. Focusing on sparse signal recovery, we concentrate on LASSO solutions known as LISTA and TISTA. These LISTA and TISTA methods, based on deep unrolling, have been devised to achieve notably faster convergence compared to ISTA. Our contribution lies in proposing secure LISTA and secure TISTA algorithms that operate on encrypted observation signals. The efficacy of the proposed approach was validated through simulations using artificially generated data for sparse signal recovery. As an illustration of the proposed methodology’s utility, we applied secure LISTA and secure TISTA to image reconstruction, to evaluate their performance.