A tuning-free alternating-minimization (AltMin) algorithm for the square-root principal component pursuit model min ||L||_* + lambda||S||_1 + mu||L+S-D||_F, in which the S- and L-subproblems each admit closed-form optimal solutions so no penalty parameter must be tuned to the unknown noise level. The paper reinterprets the model as a distributionally robust optimization problem (justifying parameter choice without separation/incoherence assumptions) and uses the nuclear-norm variational form and Burer-Monteiro factorization to accelerate the iterations, with convergence analysis and numerical validation.
The square-root principal component pursuit (SRPCP) model recovers a low-rank plus sparse matrix from corrupted data using a square-root data-fidelity term, which allows a universal, noise-level-inde…