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A Globally Convergent Algorithm for Total Scaled-Gradient Variation via Cone-Constrained Bilinear Decomposition

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edges and corners in image restoration. However, its highly nonconvex and nonlinear nature poses severe computational challenges, as existing methods often suffer from parameter sensitivity or lack convergence guarantees. To overcome this, we propose a tailored bilinear decomposition that decouples the nonlinear weighted gradient in the TSGV regularizer. This approach yields an equivalent optimization problem governed by cone or sphere constraints, dep

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