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Our goal is to obtain proximal operator of the following function $$ g \left( x \right) = {\left\| x \right\|}_{1} + \operatorname{TV}(x). $$ The involved optimization problem for any $z \in \mathbb{R}^d$ is the following $$\text{argmin}_{x}\left\{g(x) + \frac{1}{2}\|x-z\|^2_2\right\}$$ Denote the following $$g_1(x) := {\left\| x \right\|}_{1} + \frac{1}...


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Indeed the model for the Proximal Gradient Method (Also see Proximal Gradient Methods for Learning) is in the form of: $$ F \left( x \right) = f \left( x \right) + g \left( x \right) $$ Where usually $ f \left( x \right) $ is convex smooth function and $ g \left( x \right) $ is convex non smooth function. Yet the model is quite flexible and you may define ...


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