Iterative Reweighted Least Squares Networks With Convergence Guarantees for Solving Inverse Imaging Problems. (arXiv:2308.05745v1 [cs.CV])

In this work we present a novel optimization strategy for image
reconstruction tasks under analysis-based image regularization, which promotes
sparse and/or low-rank solutions in some learned transform domain. We
parameterize such regularizers using potential functions that correspond to
weighted extensions of the $\ell_p^p$-vector and $\mathcal{S}_p^p$
Schatten-matrix quasi-norms with $0 < p \le 1$. Our proposed minimization
strategy extends the Iteratively Reweighted Least Squares (IRLS) method,
typically used for synthesis-based $\ell_p$ and $\mathcal{S}_p$ norm and
analysis-based $\ell_1$ and nuclear norm regularization. …

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