A framework to generate sparsity-inducing regularizers for enhanced
  low-rank matrix completion
Zhi-Yong Wang Hing Cheung So
Applying half-quadratic optimization to loss functions can yield the
corresponding regularizers, while these regularizers are usually not
sparsity-inducing regularizers (SIRs). To solve this problem, we devise a
framework to generate an SIR with closed-form proximity operator. Besides, we
specify our framework using several commonly-used loss functions, and produce
the corresponding SIRs, which are then adopted as nonconvex rank surrogates for
low-rank matrix completion. Furthermore, algorithms based on the alternating
direction method of multipliers are developed. Extensive numerical results show
the effectiveness of our methods in terms of recovery performance and runtime.