User:Primoh/sandbox

= Iterative Shrinkage Thresholding Algorithm =

Iterative Shrinkage Thresholding Algorithm (ISTA)

Fast Iterative Shrinkage Thresholding Operator
Fast Iterative Shrinkage Thresholding Operator (FISTA)

$$ \mathbf x^{(k+1)} = \operatorname{prox}_{\gamma} [\mathbf y](\mathbf y^{(k)} - \gamma \nabla f(\mathbf y^{(k)})) $$ $$ \alpha^{(k+1)} = \frac12 (1 + \sqrt{1+4\alpha^{(k)}}) $$ $$ \mathbf y^{(k+1)} = \mathbf x^{(k)} + \frac{\alpha^{(k)}-1}{\alpha^{(k-1)}} $$

Learned Iterative Shrinkage Thresholding Operator
Learned Iterative Shrinkage Thresholding Operator (LISTA) is a

$$ \mathbf x^{(k+1)} = \mathcal S_{\gamma \lambda} (\mathbf x^{(k)} - \gamma D^T(D\mathbf x^{(k)} - \mathbf s) ) $$