New answers tagged reconstruction
3
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
$$g_1(x) := {\left\| x \right\|}_{1} + \frac{1}...
3
Indeed the model for the Proximal Gradient Method (Also see Proximal Gradient Methods for Learning) is in the form of:
$$ 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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