Alternating strategies with internal ADMM for low-rank matrix reconstruction

• Alternating optimization strategies are good for recovering matrices.
• Matrices in consideration are low-rank matrices with linear parameterized structures.
• The algorithm combines an alternating least-squares based strategy with ideas from ADMM.
• Merging these two strategies leads to a better performance and less consumed time.

This paper focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating direction method of multipliers (ADMM) to recover low-rank matrices with linear parameterized structures, such as Hankel matrices. The use of ADMM helps to improve the estimate in each iteration due to its capability of incorporating information about the direction of estimates achieved in previous iterations. We show that merging these two alternating strategies leads to a better performance and less consumed time than the existing alternating least squares (ALS) strategy. The improved performance is verified via numerical simulations with varying sampling rates and real applications.