User:Primoh/sandbox

Iterative Shrinkage Thresholding Algorithm

Iterative Shrinkage Thresholding Algorithm (ISTA)

Extensions

Fast Iterative Shrinkage Thresholding Operator

Fast Iterative Shrinkage Thresholding Operator (FISTA)

$\mathbf {x} ^{(k+1)}=\operatorname {prox} _{\gamma }[\mathbf {y} ](\mathbf {y} ^{(k)}-\gamma \nabla f(\mathbf {y} ^{(k)}))$ $\alpha ^{(k+1)}={\frac {1}{2}}(1+{\sqrt {1+4\alpha ^{(k)}}})$ $\mathbf {y} ^{(k+1)}=\mathbf {x} ^{(k)}+{\frac {\alpha ^{(k)}-1}{\alpha ^{(k-1)}}}$

Learned Iterative Shrinkage Thresholding Operator

Learned Iterative Shrinkage Thresholding Operator (LISTA) is a

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

See also

• Sparse approximation
• Proximal operator
• Iteratively reweighted least squares
• MM algorithm