Privacy Preserving Trainable ISTA using Permuted Sparse Representation

In recent years, the use of edge/cloud computing has been spreading, and sparse modeling has been attracting attention. However, in edge/cloud computing, there is a concern about the infringement of privacy due to data leakage caused by attacks or accidents. To address this concern, a secure ISTA method, which combines ISTA (one of the coefficient estimation methods of sparse modeling) with secure computation using random unitary transformations, has been proposed. The authors introduced secure TISTA, which integrates this secure arithmetic method with TISTA, an algorithm that converges to a solution more rapidly than ISTA. These algorithms can estimate the sparse coefficients while keeping the observed signal and the dictionary matrix secure. However, they have the drawback that the sparse coefficient is not secured. In noise removal or image super-resolution tasks, the sparse coefficient may represent the image after processing. Therefore, to keep the output sparse coefficients hidden from third parties, we propose secure permutation TISTA. The proposed method combines a permutation matrix with secure TISTA to secure not only the dictionary matrix and the observed signal but also the sparse coefficients.