Joint Data Compression and Parameter Estimation for Kronecker Product Structure

Due to the existence of high-dimensional data originating from observation matrices with the Kronecker product structure, it is possible to achieve cost-effective data processing by utilizing such a structure. This paper proposes an open issue, i.e., the problem of simultaneous data compression and parameter estimation for Kronecker product structure. Three joint compression-estimation schemes with different compression dimensions are derived. The first scheme is a lossless compression (LLC) estimator, where both the compressor and the estimator are Kronecker factorizable to ensure computational advantages. It shows that there is a deterministic data compression dimension equal to the rank of the observation matrix in the LLC estimator. Without satisfying this dimension, the second scheme is a general lossy compression (GLC) estimator that achieves compressed data of arbitrary dimension. The last one is a structured lossy compression estimator that reduces the number and dimension of compressed data segments suitable to special compression dimensions and has less computational burden than the GLC estimator. In addition, the performance of the three estimators is theoretically analyzed. Finally, the simulation results show the effectiveness of the proposed schemes.