On compressive self-calibration with structural constraints via alternating minimization

This paper considers the compressive bilinear self-calibration problem with explicit low-dimensional structural constraints. The celebrated proximal alternating linearized minimization (PALM) framework is adapted to simultaneously allow general sub-sampling schemes and structure-promoting regularizers. For the first time in literature, we refine the conditional convergence guarantees of PALM and show that the parameter commonly adopted to remove the scaling ambiguity as well as the structural penalties can ensure the unconditional convergence independent of strict assumptions on the statistical properties of the measurements, subspaces, number of snapshots, or initial iterates. In particular, we impose sparse and small total variation structures on the target signals and provide detailed numerical procedures for efficient computations. The extension to the complex-valued case is also made, and extensive numerical experiments are carried out to corroborate the theoretical claims. Different choices of sub-sampling schemes and compression rates are simulated to support the effectiveness of the proposed algorithm under various settings. We also make comparisons with the state-of-art competing methods, and the superiority of our proposed algorithm is empirically verified.